Doubly Degenerate Parabolic Equation with Nonlinear Inner and Boundary Sources

This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form （u^n）t = （｜ux｜^m-1ux）x ＋ u^p in （0, 1） × （0,T） subject to nonlinear boundary source （｜ux｜^m-1ux）（1,t） = u^q（1,t）, （｜ux｜^m-1ux）（0,t） = O, and positive initial data u（x,0） = uo（x）, where the parameters va, n, p, q 〉0. It is proved that the problem possesses global solutions if and only if p ≤ n and q〈min {n,m（n＋1）/m＋1}.

Atmospheric boundary layer sources for upper tropospheric air over the Asian summer monsoon region

Previous satellite measurements and model simulations have shown that the Asian summer monsoon（ASM） anticyclone is co-located with higher concentrations of pollutants, which are emitted in the continental atmospheric boundary layer（ABL）. Backward trajectory calculations show that the air at the 150-hPa level has the maximum frequency of ABL sources within 30 days over the most intensive convection regions and their downwind areas, which are not located within the ASM anticyclone,but rather at the southern flank or periphery of the ASM anticyclone. The upper tropospheric airs originated from the ABL sources include two parts： one from the ocean, which has the dominant impact to the south of 20°N, particularly over the South China Sea（SCS） and the west tropical Pacific Ocean; and another from the continent, which is dominant between 10°N and 30°N, particularly over the Bay of Bengal（BoB）, continental India, the Arabian Sea, and the Arabian Peninsula. It is the latter part that forms the higher pollutant concentration within the ASM anticyclone as shown by satellite measurements. Air in the ABL sources（both polluted and unpolluted） converges to the intensive convection region in the lower troposphere, and then traverses the middle troposphere through a wide group of upward pipes, and finally to the upper troposphere. These pipes in the middle troposphere are defined by the ASM intensive convections and cover the south of continental India,the BoB, the Tibetan Plateau, the Indochina Peninsula, the SCS, and the Philippine Sea.

The K Method for Estimating Earthquake Activity Parameters and Effect of the Boundary Uncertainty of the Source Region:Discussion on the Seismic Zoning Method

Two aspects of a new method,which can be used for seismic zoning,are introduced in this paper.On the one hand,the approach to estimate b value and annual activity rate proposed by Kijko and Sellevoll needs to use the earthquake catalogue.The existing earthquake catalogue contains both historical and recent instrumental data sets and it is inadequate to use only one part.Combining the large number of historical events with recent complete records and taking the magnitude uncertainty into account,Kijko’s method gives the maximum likelihood estimation of b value and annual activity rate,which might be more realistic.On the other hand,this method considers the source zone boundary uncertainty in seismic hazard analysis,which means the earthquake activity rate across a boundary of a source zone changes smoothly instead of abruptly and avoids too large a gradient in the calculated results.

MULTIPLICITY OF SOLUTIONS AND SOURCE TERMS IN A FOURTH ORDER NONLINEAR ELLIPTIC EQUATION

The authors investigatc relations between multiplicity of solutions and sourceterms of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition △2u＋c△u = bu+＋f inΩ, wherc Ω is a bounded open set in Rn with smoothbonndary and the nonlinearity bu+ crosses eigenvalues of △2 ＋c△. They investigate therelatiolls when the source term is constant and when it is generated by two eigenfuntions.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

Research on Design Method of the Full Form Ship with Minimum Thrust Deduction Factor

In the preliminary design stage of the full form ships, in order to obtain a hull form with low resistance and maximum propulsion efficiency, an optimization design program for a full form ship with the minimum thrust deduction factor has been developed, which combined the potential flow theory and boundary layer theory with the optimization technique. In the optimization process, the Sequential Unconstrained Minimization Technique（SUMT） interior point method of Nonlinear Programming（NLP） was proposed with the minimum thrust deduction factor as the objective function. An appropriate displacement is a basic constraint condition, and the boundary layer separation is an additional one. The parameters of the hull form modification function are used as design variables. At last, the numerical optimization example for lines of after-body of 50000 DWT product oil tanker was provided, which indicated that the propulsion efficiency was improved distinctly by this optimal design method.

The enhanced volume source boundary point method for the calculation of acoustic radiation problem

The Volume Source Boundary Point Method (VSBPM) is greatly improved so that it will speed up the VSBPM's solution of the acoustic radiation problem caused by the vibrating body. The fundamental solution provided by Helmholtz equation is enforced in a weighted residual sense over a tetrahedron located on the normal line of the boundary node to replace the coefficient matrices of the system equation. Through the enhanced volume source boundary point analysis of various examples and the sound field of a vibrating rectangular box in a semi-anechoic chamber, it has revealed that the calculating speed of the EVSBPM is more than 10 times faster than that of the VSBPM while it works on the aspects of its calculating precision and stability, adaptation to geometric shape of vibrating body as well as its ability to overcome the non-uniqueness problem.

Position optimization of particular solution sources for distributed source boundary point method by volume velocity-matching

Choosing particular solution source and its position have great influence on accu- racy of sound field prediction in distributed source boundary point method. An optimization method for determining the position of particular solution sources is proposed to get high accu- racy prediction result. In this method, tripole is chosen as the particular solution. The upper limit frequency of calculation is predicted by setting 1% volume velocity relative error limit using vibration velocity of structure surface. Then, the optimal position of particular solution sources, in which the relative error of volume velocity is minimum, is determined within the range of upper limit frequency by searching algorithm using volume velocity matching. The transfer matrix between pressure and surface volume velocity is constructed in the optimal position. After that, the sound radiation of structure is calculated by the matrix. The results of numerical simulation show that the calculation error is significantly reduced by the proposed method. When there are vibration velocity measurement errors, the calculation errors can be controlled within 5% by the method.

Evolutionary processes and sources of high-nitrate haze episodes over Beijing,Spring

Rare and consecutive high-nitrate haze pollution episodes were observed in Beijing in spring2012. We present detailed characterization of the sources and evolutionary mechanisms of this haze pollution, and focus on an episode that occurred between 15 and 26 April. Submicron aerosol species were found to be substantially elevated during haze episodes, and nitrates showed the largest increase and occupation（average： 32.2%） in non-refractory submicron particles（NR-PM1）, which did not occur in other seasons as previously reported. The haze episode（HE） was divided into three sub-episodes, HEa, HEb, and HEc. During HEa and HEc, a shallow boundary layer, stagnant meteorological conditions, and high humidity favored the formation of high-nitrate concentrations, which were mainly produced by three different processes —daytime photochemical production, gas-particle partitioning, and nighttime heterogeneous reactions — and the decline in visibility was mainly induced by NR-PM1.However, unlike HEa and HEc, during HEb, the contribution of high nitrates was partly from the transport of haze from the southeast of Beijing — the transport pathway was observed at ~800–1000 m by aerosol Lidar —and the decline in visibility during HEb was primarily caused by PM（2.5）. Our results provide useful information for air quality improvement strategies in Beijing during Spring.

Analysis on capabilities of density-based solvers within OpenFOAM to distinguish aerothermal variables in difusion boundary layer

Open source feld operation and manipulation（OpenFOAM）is one of the most prevalent open source computational fluid dynamics（CFD）software.It is very convenient for researchers to develop their own codes based on the class library toolbox within OpenFOAM.In recent years,several density-based solvers within OpenFOAM for supersonic/hypersonic compressible flow are coming up.Although the capabilities of these solvers to capture shock wave have already been verifed by some researchers,these solvers still need to be validated comprehensively as commercial CFD software.In boundary layer where diffusion is the dominant transportation manner,the convective discrete schemes＇capability to capture aerothermal variables,such as temperature and heat flux,is different from each other due to their own numerical dissipative characteristics and from viewpoint of this capability,these compressible solvers within OpenFOAM can be validated further.In this paper,frstly,the organizational architecture of density-based solvers within OpenFOAM is analyzed.Then,from the viewpoint of the capability to capture aerothermal variables,the numerical results of several typical geometrical felds predicted by these solvers are compared with both the outcome obtained from the commercial software Fastran and the experimental data.During the computing process,the Roe,AUSM＋（Advection Upstream Splitting Method）,and HLLC（Harten-Lax-van Leer-Contact）convective discrete schemes of which the spatial accuracy is 1st and 2nd order are utilized,respectively.The compared results show that the aerothermal variables are in agreement with results generated by Fastran and the experimental data even if the1st order spatial precision is implemented.Overall,the accuracy of these density-based solvers can meet the requirement of engineering and scientifc problems to capture aerothermal variables in diffusion boundary layer.

A second-order numerical method for elliptic equations with singular sources using local flter

The presence of Dirac delta function in differential equation can lead to a discontinuity,which may degrade the accuracy of related numerical methods.To improve the accuracy,a secondorder numerical method for elliptic equations with singular sources is introduced by employing a local kernel flter.In this method,the discontinuous equation is convoluted with the kernel function to obtain a more regular one.Then the original equation is replaced by this fltered equation around the singular points,to obtain discrete numerical form.The unchanged equations at the other points are discretized by using a central difference scheme.1D and 2D examples are carried out to validate the correctness and accuracy of the present method.The results show that a second-order of accuracy can be obtained in the fltering framework with an appropriate integration rule.Furthermore,the present method does not need any jump condition,and also has extremely simple form that can be easily extended to high dimensional cases and complex geometry.