26,911 research outputs found
Positive Toeplitz operators on the Bergman spaces of the Siegel upper half-space
We characterize bounded and compact positive Toeplitz operators defined on
the Bergman spaces over the Siegel upper half-space.Comment: 18 page
On the Quasitriviality of Deformations of Bihamiltonian Structures of Hydrodynamic Type
We prove in this paper the quasitriviality of a class of deformations of the
one component bihamiltonian structures of hydrodynamic type.Comment: 10 page
On Quasitriviality and Integrability of a Class of Scalar Evolutionary PDEs
For certain class of perturbations of the equation , we prove
the existence of change of coordinates, called quasi-Miura transformations,
that reduce these perturbed equations to the unperturbed ones. As an
application, we propose a criterion for the integrability of these equations.Comment: 23 page
Jacobi Structures of Evolutionary Partial Differential Equations
In this paper we introduce the notion of infinite dimensional Jacobi
structure to describe the geometrical structure of a class of nonlocal
Hamiltonian systems which appear naturally when applying reciprocal
transformations to Hamiltonian evolutionary PDEs. We prove that our class of
infinite dimensional Jacobi structures is invariant under reciprocal
transformations. The main technical tool is in a suitable generalization of the
classical Schouten-Nijenhuis bracket to the space of the so called quasi-local
multi-vectors, and a simple realization of this structure in the framework of
supermanifolds. These constructions are used to the computation of the
Lichnerowicz-Jacobi cohomologies of Jacobi structures. We also introduce the
notion of bi-Jacobi structures and consider the integrability of a system of
evolutionary PDEs that possesses a bi-Jacobi structure.Comment: 59 page
Electronic Strengthening of Graphene by Charge Doping
Graphene is known as the strongest 2D material in nature, yet we show that
moderate charge doping of either electrons or holes can further enhance its
ideal strength by up to ~17%, based on first principles calculations. This
unusual electronic enhancement, versus conventional structural enhancement, of
material's strength is achieved by an intriguing physical mechanism of charge
doping counteracting on strain induced enhancement of Kohn anomaly, which leads
to an overall stiffening of zone boundary K1 phonon mode whose softening under
strain is responsible for graphene failure. Electrons and holes work in the
same way due to the high electron-hole symmetry around the Dirac point of
graphene, while over doping may weaken the graphene by softening other phonon
modes. Our findings uncover another fascinating property of graphene with broad
implications in graphene-based electromechanical devices.Comment: 11 pages, 4 figure
The surface-forming energy release rate based fracture criterion for elastic-plastic crack propagation
J integral based criterion is widely used in elastic-plastic fracture
mechanics. However, it is not rigorously applicable when plastic unloading
appears during crack propagation. One difficulty is that the energy density
with plastic unloading in J integral cannot be defined unambiguously. In this
paper, we alternatively start from the analysis on the power balance, and
propose a surface-forming energy release rate (ERR), which represents the
energy directly dissipated on the surface-forming during the crack propagation
and excludes the loading-mode-dependent plastic dissipation. Therefore the
surface-forming ERR based fracture criterion has wider applicability, including
elastic-plastic crack propagation problems. Several formulae have been derived
for calculating the surface-forming ERR. From the most concise formula, it is
interesting to note that the surface-forming ERR can be computed only by the
stress and deformation of the current moment, and the definition of the energy
density or work density is avoided. When an infinitesimal contour is chosen,
the expression can be further simplified. For any fracture behaviors, the
surface-forming ERR is proven to be path-independent, and the path-independence
of its constituent term, so-called integral, is also investigated. The physical
meanings and applicability of the proposed surface-forming ERR, traditional
ERR, Js integral and J integral are compared and discussed
boundedness of Bergman-type operators over the Siegel upper half-space
We characterize the boundedness of Bergman-type operators over the
Siegel upper half-space. This extends a recent result of Cheng et. al. (Trans.
Amer. Math. Soc. 369:8643--8662, 2017) to higher dimensions
Solar Flares with an Exponential Growth of the Emission Measure in the Impulsive Phase Derived from X-ray Observations
The light curves of solar flares in the impulsive phase are complex in
general, indicating that multiple physical processes are involved in. With the
GOES (Geostationary Operational Environmental Satellite) observations, we find
that there are a subset of flares, whose impulsive phases are dominated by a
period of exponential growth of the emission measure. The flares occurred from
January 1999 to December 2002 are analyzed, and the results from the
observations made with both GOES 8 and GEOS 10 satellites are compared to
estimate the instrumental uncertainties. Their mean temperatures during this
exponential growth phase have a normal distribution. Most flares within the
1\sigma\ range of this temperature distribution belong to the GOES class B or
C, with the peak fluxes at the GOES low-energy channel following a log-normal
distribution. The growth rate and duration of the exponential growth phase also
follow a lognormal distribution, in which the duration is distributed in the
range from half a minute to about half an hour. As expected, the growth time is
correlated with the decay time of the soft X-ray flux. We also find that the
growth rate of the emission measure is strongly anti-correlated with the
duration of the exponential growth phase, and the mean temperature increases
slightly with the increase of the growth rate. The implications of these
results on the study of energy release in solar flares are discussed in the
end.Comment: 10 figure
Modelling imbibition processes in heterogeneous porous media
Imbibition is a commonly encountered multiphase problem in various fields,
and exact prediction of imbibition processes is a key issue for better
understanding capillary flow in heterogeneous porous media. In this work, a
numerical framework for describing imbibition processes in porous media with
material heterogeneity is proposed to track the moving wetting front with the
help of a partially saturated region at the front vicinity. A new interface
treatment, named the interface integral method, is developed here, combined
with which the proposed numerical model provides a complete framework for
imbibition problems. After validation of the current model with existing
experimental results of one-dimensional imbibition, simulations on a series of
two-dimensional cases are analysed with the presences of multiple porous
phases. The simulations presented here not only demonstrate the suitability of
the numerical framework on complex domains but also present its feasibility and
potential for further engineering applications involving imbibition in
heterogeneous media.Comment: 8 figure
Central Invariants of the Constrained KP Hierarchies
We compute the central invariants of the bihamiltonian structures of the
constrained KP hierarchies, and show that these integrable hierarchies are
topological deformations of their hydrodynamic limits.Comment: 20 page
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