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 $u_t=f(u) u_x$, 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

Lp−LqL^p-L^q boundedness of Bergman-type operators over the Siegel upper half-space

We characterize the $L^p-L^q$ 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