1,125 research outputs found
Mixed mode pattern in Doublefoot mutant mouse limb - Turing reaction-diffusion model on a growing domain during limb development
It has been suggested that the Turing reaction–diffusion model on a growing domain is applicable during limb development, but experimental evidence for this hypothesis has been lacking. In the present study, we found that in Doublefoot mutant mice, which have supernumerary digits due to overexpansion of the limb bud, thin digits exist in the proximal part of the hand or foot, which sometimes become normal abruptly at the distal part. We found that exactly the same behaviour can be reproduced by numerical simulation of the simplest possible Turing reaction–diffusion model on a growing domain. We analytically showed that this pattern is related to the saturation of activator kinetics in the model. Furthermore, we showed that a number of experimentally observed phenomena in this system can be explained within the context of a Turing reaction–diffusion model. Finally, we make some experimentally testable predictions
Lectures on the Asymptotic Expansion of a Hermitian Matrix Integral
In these lectures three different methods of computing the asymptotic
expansion of a Hermitian matrix integral is presented. The first one is a
combinatorial method using Feynman diagrams. This leads us to the generating
function of the reciprocal of the order of the automorphism group of a tiling
of a Riemann surface. The second method is based on the classical analysis of
orthogonal polynomials. A rigorous asymptotic method is established, and a
special case of the matrix integral is computed in terms of the Riemann
-function. The third method is derived from a formula for the
-function solution to the KP equations. This method leads us to a new
class of solutions of the KP equations that are
\emph{transcendental}, in the sense that they cannot be obtained by the
celebrated Krichever construction and its generalizations based on algebraic
geometry of vector bundles on Riemann surfaces. In each case a mathematically
rigorous way of dealing with asymptotic series in an infinite number of
variables is established
Bispectral KP Solutions and Linearization of Calogero-Moser Particle Systems
A new construction using finite dimensional dual grassmannians is developed
to study rational and soliton solutions of the KP hierarchy. In the rational
case, properties of the tau function which are equivalent to bispectrality of
the associated wave function are identified. In particular, it is shown that
there exists a bound on the degree of all time variables in tau if and only if
the wave function is rank one and bispectral. The action of the bispectral
involution, beta, in the generic rational case is determined explicitly in
terms of dual grassmannian parameters. Using the correspondence between
rational solutions and particle systems, it is demonstrated that beta is a
linearizing map of the Calogero-Moser particle system and is essentially the
map sigma introduced by Airault, McKean and Moser in 1977.Comment: LaTeX, 24 page
A Plasma {\beta} Transition Within a Propagating Flux Rope
We present a 2.5D MHD simulation of a magnetic flux rope (FR) propagating in
the heliosphere and investigate the cause of the observed sharp plasma beta
transition. Specifically, we consider a strong internal magnetic field and an
explosive fast start, such that the plasma beta is significantly lower in the
FR than the sheath region that is formed ahead. This leads to an unusual FR
morphology in the first stage of propagation, while the more traditional view
(e.g. from space weather simulations like Enlil) of a `pancake' shaped FR is
observed as it approaches 1 AU. We investigate how an equipartition line,
defined by a magnetic Weber number, surrounding a core region of a propagating
FR can demarcate a boundary layer where there is a sharp transition in the
plasma beta. The substructure affects the distribution of toroidal flux, with
the majority of the flux remaining in a small core region which maintains a
quasi-cylindrical structure. Quantitatively, we investigate a locus of points
where the kinetic energy density of the relative inflow field is equal to the
energy density of the transverse magnetic field (i.e. effective tension force).
The simulation provides compelling evidence that at all heliocentric distances
the distribution of toroidal magnetic flux away from the FR axis is not linear;
with 80% of the toroidal flux occurring within 40% of the distance from the FR
axis. Thus our simulation displays evidence that the competing ideas of a
pancaking structure observed remotely can coexist with a quasi-cylindrical
magnetic structure seen in situ.Comment: 11 pages of text + 6 figures. Accepted to ApJ on 16 Oct 201
Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy
Pairs of matrices whose commutator differ from the identity by a
matrix of rank are used to construct bispectral differential operators with
matrix coefficients satisfying the Lax equations of the Matrix KP
hierarchy. Moreover, the bispectral involution on these operators has dynamical
significance for the spin Calogero particles system whose phase space such
pairs represent. In the case , this reproduces well-known results of
Wilson and others from the 1990's relating (spinless) Calogero-Moser systems to
the bispectrality of (scalar) differential operators. This new class of pairs
of bispectral matrix differential operators is different than
those previously studied in that acts from the left, but from the
right on a common eigenmatrix.Comment: 16 page
Suzaku observations of Jovian diffuse hard X-ray emission
We report on results of systematic analyses of the entire three X-ray data sets of Jupiter taken by Suzaku in 2006, 2012, and 2014. Jovian diffuse hard X-ray emission was discovered by Suzaku in 2006 when the solar activity went toward its minimum. The diffuse emission was spatially consistent with the Jovian inner magnetosphere and was spectrally fitted with a flat power-law function suggesting non-thermal emission. Thus, a scenario in which ultra-relativistic (tens of MeV) electrons in the Jovian inner magnetosphere inverse-Comptonize solar visible photons into X-ray bands has been hypothetically proposed. We focused on the dependence of the Jovian diffuse hard X-ray emission on the solar activity to verify this scenario. The solar activity in 2012 and 2014 was around the maximum of the 24th solar cycle. By combining the imaging and spectral analyses for the three data sets, we successfully separated the contribution of the diffuse emission from the emission of Jupiter’s body (i.e., the aurora and disk emission). The 1–5 keV luminosity of the diffuse emission has been stable and did not vary significantly, and did not simply depend on the solar activity, which is also known to affect the high-energy electron distribution in the Jovian inner magnetosphere scarcely. The luminosity of the body emission both in 0.2–1 and 1–5 keV, in contrast, probably depended on the solar activity and varied by a factor of 2–5. These results strongly supported the inverse-Compton scattering scenario by the ultra-relativistic electrons. In this paper, we estimate spatial and spectral distributions of the inverse-Compton scattering X-rays by Jovian magnetospheric high-energy electrons with reference to the Divine–Garrett model and found a possible agreement in an inner region (≲10 RJ) for the X-ray observations
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