1,761 research outputs found
A novel multi-component generalization of the short pulse equation and its multisoliton solutions
We propose a novel multi-component system of nonlinear equations that
generalizes the short pulse (SP) equation describing the propagation of
ultra-short pulses in optical fibers. By means of the bilinear formalism
combined with a hodograph transformation, we obtain its multi-soliton solutions
in the form of a parametric representation. Notably, unlike the determinantal
solutions of the SP equation, the proposed system is found to exhibit solutions
expressed in terms of pfaffians. The proof of the solutions is performed within
the framework of an elementary theory of determinants. The reduced 2-component
system deserves a special consideration. In particular, we show by establishing
a Lax pair that the system is completely integrable. The properties of
solutions such as loop solitons and breathers are investigated in detail,
confirming their solitonic behavior. A variant of the 2-component system is
also discussed with its multisoliton solutions.Comment: Minor correction
Thermal conductivity of the thermoelectric layered cobalt oxides measured by the Harman method
In-plane thermal conductivity of the thermoelectric layered cobalt oxides has
been measured using the Harman method, in which thermal conductivity is
obtained from temperature gradient induced by applied current. We have found
that the charge reservoir block (the block other than the CoO block)
dominates the thermal conduction, where a nano-block integration concept is
effective for material design. We have further found that the thermal
conductivity shows a small but finite in-plane anisotropy between and
axes, which can be ascribed to the misfit structure.Comment: 4 pages, 4 figures, J. Appl. Phys. (scheduled on July 1, 2004
On the geometry of Siegel-Jacobi domains
We study the holomorphic unitary representations of the Jacobi group based on
Siegel-Jacobi domains. Explicit polynomial orthonormal bases of the Fock spaces
based on the Siegel-Jacobi disk are obtained. The scalar holomorphic discrete
series of the Jacobi group for the Siegel-Jacobi disk is constructed and
polynomial orthonormal bases of the representation spaces are given.Comment: 15 pages, Latex, AMS fonts, paper presented at the the International
Conference "Differential Geometry and Dynamical Systems", August 25-28, 2010,
University Politehnica of Bucharest, Romani
Understanding Circadian Regulation of Carbohydrate Metabolism in Arabidopsis Using Mathematical Models
C3 plants assimilate carbon by photosynthesis only during
the day, but carbon resources are also required for growth
and maintenance at night. To avoid carbon starvation, many
plants store a part of photosynthetic carbon in starch during
the day, and degrade it to supply sugars for growth at night.
In Arabidopsis, starch accumulation in the day and degradation
at night occur almost linearly, with the shape of this
diel starch profile adaptively changing to allow continuous
supply of sugar even in long-night conditions. The anticipation
of dawn required to ensure linear consumption of
starch to almost zero at dawn presumably requires the circadian
clock. We review the links between carbon metabolism
and the circadian clock, and mathematical models
aimed at explaining the diel starch profile. These models
can be considered in two classes, those that assume the
level of available starch is sensed and the system ensures
linearity of starch availability, and those in which sugar sensing
is assumed, yielding linearity of starch availability as an
emergent property of sucrose homeostasis. In the second
class of model the feedback from starch metabolism to the
circadian clock is considered to be essential for adaptive
response to diverse photoperiods, consistent with recent
empirical data demonstrating entrainment of the circadian
clock by photosynthesis. Knowledge concerning the mechanisms
regulating the dynamics of starch metabolism and
sugar homeostasis in plants is required to develop new
theories about the limitations of growth and biomass
accumulation
Neoclassical Toroidal Viscosity Calculations in Tokamaks Using a δf Monte Carlo Simulation and Their Verifications
Neoclassical toroidal viscosities (NTVs) in tokamaks are investigated using a δf Monte Carlo simulation, and are successfully verified with a combined analytic theory over a wide range of collisionality. A Monte Carlo simulation has been required in the study of NTV since the complexities in guiding-center orbits of particles and their collisions cannot be fully investigated by any means of analytic theories alone. Results yielded the details of the complex NTV dependency on particle precessions and collisions, which were predicted roughly in a combined analytic theory. Both numerical and analytic methods can be utilized and extended based on these successful verifications
Dependence of Radial Thermal Diffusivity on Parameters of Toroidal Plasma Affected by Resonant Magnetic Perturbations (II)
- …