13,143 research outputs found
On the Boltzmann equation with the symmetric stable Levy process
As for the spatially homogeneous Boltzmann equation of Maxwellian molecules
with the fractional Fokker-Planck diffusion term, we consider the Cauchy
problem for its Fourier-transformed version, which can be viewed as a kinetic
model for the stochastic time-evolution of characteristic functions associated
with the symmetric stable Levy process and the Maxwellian collision dynamics.
Under a non-cutoff assumption on the kernel, we establish a global existence
theorem with maximum growth estimate, uniqueness and stability of solutions.Comment: in Kinetic and Related Models, 201
Local Existence for the Spatially Homogeneous Boltzmann Equation with Soft Potentials
We prove a local-in-time existence and uniqueness theorem for a smooth
classical solution to the spatially homogeneous Boltzmann equation with cutoff
soft potentials. Our proof is based on a series of bilinear estimates for the
integrability and Sobolev regularity of the associated collision operator.
While the global-in-time existence is left inconclusive, we give a lower bound
of the maximal time of existence and a necessary condition for finite time
extinction of existence.Comment: in Kinetic and Related Models, 201
Absolute moments and Fourier-based probability metrics
We present a family of explicit formulae for evaluating absolute moments of
probability measures on in terms of Fourier transforms. As to
the space of probability measures possessing finite absolute moments of an
arbitrary order, we exploit our formulae to characterize its Fourier image and
construct Fourier-based probability metrics which make the space complete. As
applications, we compute absolute moments of those probability measures whose
characteristic functions belong to the Scheonberg classes, estimate absolute
moments of convolutions and investigate the asymptotic behavior of solutions to
the heat-diffusion equations from a probability view-point
Real-space Hamiltonian method for low-dimensional semiconductor heterostructures
We present a new method for calculating electronic states in low-dimensional
semiconductor heterostructures, which is based on the real-space Hamiltonian in
the envelope function approximation. The numerical implementation of the method
is extremely simple; all subband energy levels and envelope functions are
directly obtained by a single evaluation of the heterostructure Hamiltonian
matrix. We test the method in the 6- and 8-band k \cdot p models as well as in
a simple parabolic one-band model and demonstrate its great accuracy. The
method can be straightforwardly generalized to a general n-band k \cdot p
model. We describe three different approaches within the method which make it
possible to investigate the origin and removal of the spurious or unphysical
solutions, which has long been an important issue in the community.Comment: 44 pages, 15 figure
Newton diagram of positivity for generalized hypergeometric functions
As for the positivity of generalized hypergeometric functions, we
present a list of necessary and sufficient conditions in terms of parameters
and determine the region of positivity by certain Newton diagram.Comment: 19 pages, 3 figure
Locality of the overlap-Dirac operator on topology-fixed gauge configurations
We investigate the locality property of the overlap-Dirac operator on gauge
configurations generated with extra Wilson fermions. By such extra terms we
expect that the structure of the Aoki phase would change drastically. In
particular, we study the possibility of defining the overlap-Dirac operator in
the strong coupling regime keeping its exponential locality.Comment: 7 pages, 5 figures, Proceedings of the 30th International Symposium
on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australi
Morse theory in path space
We consider the path space of a curved manifold on which a point particle is
introduced in a conservative physical system with constant total energy to
formulate its action functional and geodesic equation together with breaks on
the path. The second variation of the action functional is exploited to yield
the geodesic deviation equation and to discuss the Jacobi fields on the curved
manifold. We investigate the topology of the path space using the action
functional on it and its physical meaning by defining the gradient of the
action functional, the space of bounded flow energy solutions and the moduli
space associated with the critical points of the action functional. We also
consider the particle motion on the -sphere in the conservative
physical system to discuss explicitly the moduli space of the path space and
the corresponding homology groups.Comment: 6 page
Spin-polarized bandgap of graphene induced by alternative chemisorption with MgO (111) substrate
Using First-principle calculations, substrate effect of O-terminated (rt3 x
rt3) MgO (111) on graphene was investigated for spintronics application.
Surprisingly, the graphene can be turned into a spin-polarized semiconductor,
which implies that the totally spin-polarized current can be generated and its
on/off switching can be also controlled. The origin of the spin-polarized band
structure is spin-ordering due to alternative sp2-sp3 covalent bondings induced
by the MgO (111) substrate. The results indicate that the tailored pattern of
the chemisorption can be highly efficient or introducing totally spin-polarized
current to the graphene.Comment: This paper has been withdrawn due to a crucial typo in the Figure
Dynamics of stringy congruence in early universe
We studied the singularity of the geodesic surface congruence for timelike
and null strings using the expansion of the universe in the string theory. We
had Raychaudhuri type equation for the expansion. Assuming the stringy strong
energy condition and initial convergence, we induced the existence of
singularity and got the same inequality equation of the string strong energy
condition for both timelike and null stringy congruence. In this paper we want
to study the twist and shear aspects of the stingy geodesic surface congruence.
Under some natural conditions we derive the equations of the twist and the
shear in terms of the expansion of the universe. In appendix we investigate the
geodesic surface congruence of the null strings.Comment: 11 page
String reveals secrets of universe
Stringy cosmology displays features that are different from standard
cosmology. One may be surprised in that in this scenario there is no phase
transition between the radiation dominated phase and matter dominated phase and
the universe is cyclic similar to brane cyclic cosmology.Comment: 2 page
- β¦