26,689 research outputs found
An advanced meshless method for time fractional diffusion equation
Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations
Scattering on two Aharonov-Bohm vortices with opposite fluxes
The scattering of an incident plane wave on two Aharonov-Bohm vortices with
opposite fluxes is considered in detail. The presence of the vortices imposes
non-trivial boundary conditions for the partial waves on a cut joining the two
vortices. These conditions result in an infinite system of equations for
scattering amplitudes between incoming and outgoing partial waves, which can be
solved numerically. The main focus of the paper is the analytic determination
of the scattering amplitude in two limits, the small flux limit and the limit
of small vortex separation. In the latter limit the dominant contribution comes
from the S-wave amplitude. Calculating it, however, still requires solving an
infinite system of equations, which is achieved by the Riemann-Hilbert method.
The results agree well with the numerical calculations
A Cosmological Model with Dark Spinor Source
In this paper, we discuss the system of Friedman-Robertson-Walker metric
coupling with massive nonlinear dark spinors in detail, where the thermodynamic
movement of spinors is also taken into account. The results show that, the
nonlinear potential of the spinor field can provide a tiny negative pressure,
which resists the Universe to become singular. The solution is oscillating in
time and closed in space, which approximately takes the following form
g_{\mu\nu}=\bar R^2(1-\delta\cos t)^2\diag(1,-1,-\sin^2r ,-\sin^2r
\sin^2\theta), with light year, and
. The present time is about .Comment: 13 pages, no figure, to appear in IJMP
Effective generation of Ising interaction and cluster states in coupled microcavities
We propose a scheme for realizing the Ising spin-spin interaction and atomic
cluster states utilizing trapped atoms in coupled microcavities. It is shown
that the atoms can interact with each other via the exchange of virtual photons
of the cavities. Through suitably tuning the parameters, an effective Ising
spin-spin interaction can be generated in this optical system, which is used to
produce the cluster states. This scheme does not need the preparation of
initial states of atoms and cavity modes, and is insensitive to cavity decay.Comment: 11pages, 2 figures, Revtex
Upper Pseudogap Phase: Magnetic Characterizations
It is proposed that the upper pseudogap phase (UPP) observed in the high-Tc
cuprates correspond to the formation of spin singlet pairing under the bosonic
resonating-valence-bond (RVB) description. We present a series of evidence in
support of such a scenario based on the calculated magnetic properties
including uniform spin susceptibility, spin-lattice and spin-echo relaxation
rates, which consistently show that strong spin correlations start to develop
upon entering the UPP, being enhanced around the momentum (\pi, \pi) while
suppressed around (0, 0). The phase diagram in the parameter space of doping
concentration, temperature, and external magnetic field, is obtained based on
the the bosonic RVB theory. In particular, the competition between the Zeeman
splitting and singlet pairing determines a simple relation between the
"critical" magnetic field, H_{PG}, and characteristic temperature scale, T0, of
the UPP. We also discuss the magnetic behavior in the lower pseudogap phase at
a temperature Tv lower than T0, which is characterized by the formation of
Cooper pair amplitude where the low-lying spin fluctuations get suppressed at
both (0, 0) and (\pi, \pi). Properties of the UPP involving charge channels
will be also briefly discussed.Comment: 11 pages, 5 figures, final version to appear in PR
Neutrino masses, leptogenesis and dark matter in hybrid seesaw
We suggest a hybrid seesaw model where relatively ``light''right-handed
neutrinos give no contribution to the neutrino mass matrix due to a special
symmetry. This allows their Yukawa couplings to the standard model particles to
be relatively strong, so that the standard model Higgs boson can decay
dominantly to a left and a right-handed neutrino, leaving another stable
right-handed neutrino as cold dark matter. In our model neutrino masses arise
via the type-II seesaw mechanism, the Higgs triplet scalars being also
responsible for the generation of the matter-antimatter asymmetry via the
leptogenesis mechanism.Comment: 4 page
Magneto-infrared spectroscopy of Landau levels and Zeeman splitting of three-dimensional massless Dirac Fermions in ZrTe
We present a magneto-infrared spectroscopy study on a newly identified
three-dimensional (3D) Dirac semimetal ZrTe. We observe clear transitions
between Landau levels and their further splitting under magnetic field. Both
the sequence of transitions and their field dependence follow quantitatively
the relation expected for 3D \emph{massless} Dirac fermions. The measurement
also reveals an exceptionally low magnetic field needed to drive the compound
into its quantum limit, demonstrating that ZrTe is an extremely clean
system and ideal platform for studying 3D Dirac fermions. The splitting of the
Landau levels provides a direct and bulk spectroscopic evidence that a
relatively weak magnetic field can produce a sizeable Zeeman effect on the 3D
Dirac fermions, which lifts the spin degeneracy of Landau levels. Our analysis
indicates that the compound evolves from a Dirac semimetal into a topological
line-node semimetal under current magnetic field configuration.Comment: Editors' Suggestio
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