EVOLUTION FILTRATION PROBLEMS WITH SEAWATER INTRUSION: TWO-PHASE FLOW DUAL MIXED VARIATIONAL ANALYSIS

Tow-phase flow mixed variational formulations of evolution filtration problems with seawater intrusion are analyzed. A dual mixed fractional flow velocity-pressure model is considered with an air-fresh water and a fresh water-seawater characterization. For analysis and computational purposes, spatial decompositions based on nonoverlapping multidomains, above and below the sea level, are variationally introduced with internal boundary fluxes dualized as weak transmission constraints. Further, parallel augmented and exactly penalized duality algorithms, and proximation semi-implicit time marching schemes, are established and analyzed.

Variational analysis of thermomechanically coupled steady-state rolling problem

A steady-state, rigid-plastic rolling problem for temperature and strain-rate dependent materials with nonlocal friction is considered. A variational formulation is derived, coupling a nonlinear variational inequality for the velocity and a nonlinear vari- ational equation for the temperature. The existence and uniqueness results are obtained by a proposed fixed point method.

Two-Dimensional Variational Analysis of Near-Surface Moisture from Simulated Radar Refractivity-Related Phase Change Observations

Because they are most sensitive to atmospheric moisture content, radar refractivity observations can provide high-resolution information about the highly variable low-level moisture field. In this study, simulated radar refractivity-related phase-change data were created using a radar simulator from realistic highresolution model simulation data for a dryline case. These data were analyzed using the 2DVAR system developed specifically for the phase-change data. Two sets of experiments with the simulated observations were performed, one assuming a uniform target spacing of 250 m and one assuming nonuniform spacing between 250 m to 4 km. Several sources of observation error were considered, and their impacts were examined. They included errors due to ground target position uncertainty, typical random errors associated with radar measurements, and gross error due to phase wrapping. Without any additional information, the 2DVAR system was incapable of dealing with phase-wrapped data directly. When there was no phase wrapping in the data, the 2DVAR produced ex- cellent analyses, even in the presence of both position uncertainty and random radar measurement errors. When a separate pre-processing step was applied to unwrap the phase-wrapped data, quality moisture anal- yses were again obtained, although the analyses were smoother due to the reduced effective resolution of the observations by interpolation and smoothing involved in the unwrapping procedure. The unwrapping procedure was effective even when significant differences existed between the analyzed state and the state at a reference time. The results affirm the promise of using radar refractivity phase-change measurements for near-surface moisture analysis.

Generalized Method of Variational Analysis for 3-D Flow

The generalized method of variational analysis (GMVA) suggested for 2-D wind observations by Huang et al. is extended to 3-D cases. Just as in 2-D cases, the regularization idea is applied. But due to the complexity of the 3-D cases, the vertical vorticity is taken as a stable functional. The results indicate that wind observations can be both variationally optimized and ?ltered. The e?ciency of GMVA is also checked in a numerical test. Finally, 3-D wind observations with random disturbances are manipulated by GMVA after being ?ltered.

Variational Reconstruction and Simulation Experiments of Sea Surface Wind Field for Ocean Data Buoy

The sea surface wind field is an important physical parameter in oceanography and meteorology.With the continuous refinement of numerical weather prediction,air-sea interface materials,energy exchange,and other studies,three-dimensional(3D)wind field distribution at local locations on the sea surface must be measured accurately.The current in-situ observation of sea surface wind parameters is mainly achieved through the installation of wind sensors on ocean data buoys.However,the results obtained from this single-point measurement method cannot reflect wind field distribution in a vertical direction above the sea surface.Thus,the present paper proposes a theoretical framework for the optimal inversion of the 3D wind field structure variation in the area where the buoy is located.The variation analysis method is first used to reconstruct the wind field distribution at different heights of the buoy,after which theoretical analysis verification and numerical simulation experiments are conducted.The results indicate that the use of variational methods to reconstruct 3D wind fields is significantly effective in eliminating disturbance errors in observations,which also verifies the correctness of the theoretical analysis of this method.The findings of this article can provide a reference for the layout optimization design of wind measuring instruments in buoy observation systems and also provide theoretical guidance for the design of new observation buoys in the future.

A MIXED VARIATIONAL FORMULATION FOR LARGE DEFORMATION ANALYSIS OF PLATES

A mixed vuriational formulation for large deformation analysis of plates is introduced. In this formulation the equilibrium ami compatibility equations are satisfied identically by means of stress functions and displacement components, respectively, and the constitu,lye equations are satisfied in a least square sense. An example is solved and the results are compared with those available in the literature.Further, the functional is particularized for buckling analysis of plates and a simple example is solved to illustrate the theory.

DISCUSSION OF CRITICAL LOAD IN NONLINEAR STABILITY ANALYSIS AND SUGGESTION OF VARIATIONAL PRINCIPLE OF SOLVING CRITICAL LOADS

In this paper, a set of variational formulas of solving nonlinear instability critical loads are established from the viewpoint of variational principle. The paper shows that it is very convenient to solve nonlinear instability critical load by using the variational formulas suggested in this paper.

Three-dimensional limit variation analysis on the ultimate pullout capacity of the anchor cables based on the Hoek-Brown failure criterion

Only simplified two-dimensional model and a single failure mode are adopted to calculate the ultimate pullout capacity(UPC)of anchor cables in most previous research.This study focuses on a more comprehensive combination failure mode that consists of bond failure of an anchorage body and failure of an anchored rock mass.The three-dimensional ultimate pullout capacity of the anchor cables is calculated based on the Hoek-Brown failure criterion and variation analysis method.The numerical solution for the curvilinear function in fracture plane is obtained based on the finite difference theory,which more accurately reflects the failure state of the anchor cable,as opposed to that being assumed in advance.The results reveal that relying solely on a single failure mode for UPC calculations has limitations,as changes in parameter values not only directly impact the UPC value but also can alter the failure model and thus the calculation method.

Genetic Variation Analysis of 3D Gene and Molecular Detection of Porcine Kobuvirus in 2013-2014

[Objective] This study aimed to investigate the prevalence and variation of porcine kobuvirus （PKV） in suckling piglets in China. [Method] In 2013-2014, 224 feces samples from suckling piglets with diarrhea in 27 pig farms of five provinces in China were collected to detect 3D genes of PKV with RT-PCR method; the sequences and genetic variation of 29 PKV 3D genes were analyzed. [Result] Total positive rate of PKV in feces samples from suckling piglets with diarrhea was 65.18% （146/224）; total positive rate of PKV in pig farms was 85,2% （23/27）; nucleotide sequences and the deduced amino acid sequences of 29 PKV 3D genes shared 87.0%-100% and 92.7%-100% homologies with six PKV-related 3D sequences, respectively. [Conclusion] PKV infection is prevalent in suckling piglets in China; PKV 3D genes exhibit high diversity.

Analysis of the Maximum Consecutive Precipitation Variation in Liaoning Artificial Precipitation Test Area

According to the daily precipitation data in artificial precipitation season during May to September from 1961 to 2008 in Liaoning Province,the maximum consecutive precipitation in the artificial precipitation test area is studied based on the maximum consecutive precipitation from May to September in 48 years.The results shows that the period of maximum consecutive precipitation in each month is different,and the variance trends of maximum consecutive precipitation in May,July,August and September are decreasing,while the variance trend of maximum consecutive precipitation in June is increasing.

Variation analysis of ultimate pullout capacity of shallow horizontal strip anchor plate with 2-layer overlying soil based on nonlinear M-C failure criterion

Based on the nonlinear Mohr-Coulomb failure criterion and an associated flow rule,a kinematic admissible velocity field of failure mechanism of the 2-layer soil above a shallow horizontal strip anchor plate is constructed.The ultimate pull-out force and its corresponding failure mechanism through the upper bound limit analysis according to a variation principle are deduced.When the 2-layer overlying soil is degraded into single-layer soil,the model of ultimate pullout force could also be degraded into the model of single-layer soil.And the comparison between results of single-layer soil variation method and those calculated by rigid limit analysis method proves the correctness of our method.Based on that,the influence of changes of geotechnical parameters on ultimate pullout forces and failure mechanism of a shallow horizontal strip anchor with the 2-layer soil above are analyzed.The results show that the ultimate pull-out force and failure mechanism of a shallow horizontal strip anchor with the 2-layer soil above are affected by the nonlinear geotechnical parameters greatly.Thus,it is very important to obtain the accurate geotechnical parameters of 2-layer soil for the evaluation of the ultimate pullout capacity of the anchor plate.

Upper bound analysis of ultimate pullout capacity of shallow 3-D circular plate anchors based on nonlinear Mohr-Coulomb failure criterion

Based on the nonlinear Mohr-Coulomb failure criterion and the associated flow rules,the three-dimensional(3-D)axisymmetric failure mechanism of shallow horizontal circular plate anchors that are subjected to the ultimate pullout capacity(UPC)is determined.A derivative function of the projection function for projecting the 3-D axisymmetric failure surface on plane is deduced using the variation theory.By using difference principle,the primitive function of failure surface satisfying boundary condition and numerical solution to its corresponding ultimate pullout capacity function are obtained.The influences of nonlinear Mohr-Coulomb parameters on UPC and failure mechanism are studied.The result shows that UPC decreases with dimensionless parameter m and uniaxial tensile strength increases but increases when depth and radius of plate anchor,surface overload,initial cohesion,geomaterial density and friction angle increase.The failure surface is similar to a symmetrical spatial funnel,and its shape is mainly determined by dimensionless parameter m;the surface damage range expands with the increase of radius and depth of the plate anchor as well as initial cohesion but decreases with the increase of dimensionless parameter m and uniaxial tensile strength as well as geomaterial density.As the dimensionless parameter m=2.0,the numerical solution of UPC based on the difference principle is proved to be feasible and effective through the comparison with the exact solution.In addition,the comparison between solutions of UPC computed by variation method and those computed by upper bound method indicate that variation method outperforms upper bound method.

Variation Analysis of Seed and Seedling Traits of Cross Combination Progenies in Populus

Twenty-five species and hybrids in Populus were used as parents, and 26 cross combinations, including more than 5000 seedlings, were obtained by artificial cross breeding. The length of infructescence, number of seeds per infructescence, thousand-seed weight, germination rate of seeds among these cross combinations were tested. The results indicated that the cross combinational effects were significant for these traits, and demonstrated that the length of infructescence, thousand-seed weight were positively affected by female parent. In addition, seedling height, diameter above ground, diameter at breast height （DBH） of 17 cross combination progenies were investigated. The analysis of mean and standard deviation of these three traits showed that seedling height, diameter above ground, DBH had extensive variation among combinations and individuals within combination. Variance analysis and estimate of heritability indicated that the three traits had wide variation and were controlled by heredity. It was feasible to select superior cross combinations and seedlings. Further more, the result of multiple comparison showed that P.deltoides ‘Lux＇× P.deltoides ‘D324＇, P.ussuriensis cl. ‘U4＇× P deltoides ‘T66＇, P.ussuriensis cl. ‘U4＇× P. deltoides ‘T26＇, P.deltoides ‘Lux＇× P.ussuriensis cl. ‘U3＇, （P.tomentosa×P.bolleana）×（P.alba×P.glandulosa）, （P.alba×P.tomentosa）×（P.alba×P.glandulosa）, and （P.alba×P.glandulosa‘No.2＇）× P. tomentosa ‘Lumao 50＇ were superior cross combinations with higher growth rate. Finally, 123 elite seedlings were selected for further test.

Preliminary Analysis of Climatic Variation during the Last 39 Years in China

The preliminary analysis of climatic variation in China during the last 39 years has been made in this paper. The results show that although the global climate is getting warmer, some parts of China are cooling. The warming only occurs in Northeast, North and the west part of Northwest China while the areas between about 35°N and Nanling Mountain, east of the Tibetan Plateau in China are getting cooler. The cooling centers are located in Sichuan, the south part of Shaanxi and the north part of Yunnan respectively. According to the theory of greenhouse effect, there are much precipitation at low and high latitudes and less precipitation in middle latitude. However, the precipitation in the most parts of China has been decreased, especially in North and Northwest China.

Limit variation analysis of shallow rectangular tunnels collapsing with double-layer rock mass based on a three-dimensional failure mechanism

In the framework of upper bound theorem of limit analysis, the progressive collapse of shallow rectangular tunnels with double-layer rock mass has been theoretically analyzed based on the three-dimensional (3D) velocity discontinuity surfaces. According to the virtual work principle, the difference theorem and the variation method, the collapse surface of double-layer rock mass is determined based on the Hoek-Brown failure criterion. The formula can be degenerated to a single-layer rock collapsing problem when the rock mass is homogeneous. To estimate the validity of the result, the numerical simulation software PLAXIS 3D is used to simulate the collapse of shallow tunnels with double-layer rock mass, and the comparative analysis shows that numerical results are in good agreement with upper-bound solutions. According to the results of parametric analysis, the potential range of collapse of a double-layer rock mass above a shallow cavity decreases with a decrease in A1/A2,σci1/σci2 and σtm1/σtm2 and an increase in B1/B2,γ1/γ2. The range will decrease with a decrease in support pressure q and increase with a decrease in surface overload σs. Therefore, reinforced supporting is beneficial to improve the stability of the cavity during actual construction.

Application of the Tikhonov regularization method to wind retrieval from scatterometer data I.Sensitivity analysis and simulation experiments

Scatterometer is an instrument which provides all-day and large-scale wind field information, and its application especially to wind retrieval always attracts meteorologists. Certain reasons cause large direction error, so it is important to find where the error mainly comes. Does it mainly result from the background field, the normalized radar cross-section （NRCS） or the method of wind retrieval？ It is valuable to research. First, depending on SDP2.0, the simulated ＇true＇ NRCS is calculated from the simulated ＇true＇ wind through the geophysical mode] function NSCAT2. The simulated background field is configured by adding a noise to the simulated ＇true＇ wind with the non-divergence constraint. Also, the simulated ＇measured＇ NRCS is formed by adding a noise to the simulated ＇true＇ NRCS. Then, the sensitivity experiments are taken, and the new method of regularization is used to improve the ambiguity removal with simulation experiments. The results show that the accuracy of wind retrieval is more sensitive to the noise in the background than in the measured NRCS; compared with the two-dimensional variational （2DVAR） ambiguity removal method, the accuracy of wind retrieval can be improved with the new method of Tikhonov regularization through choosing an appropriate regularization parameter, especially for the case of large error in the background. The work will provide important information and a new method for the wind retrieval with real data.

MESO-MECHANICAL ANALYSIS OF SHAPE MEMORY ALLOY REINFORCED SMART STRUCTURE WITH DAMAGE

The mechanical behaviors of shape memory alloy （SMA） wires reinforced smart structure with damage were analyzed through the variational principle, a governing equation for the structure was derived, mathematical expressions for the meso-displacement field, stressstrain field of typical element with damage were presented, and a failure criterion for interface failure between SMA wires and matrix was established under two kinds of actuation which are dead-load and temperature, where the temperature is included in effective free restoring strain. In addition, there are some other composing factors in the failure criterion such as the interface properties, dynamical properties of SMA, initial debonding length L - l etc. The results are significant to understand structural strength self-adapted control and failure mechanism of SMA wires reinforced smart structure with damage.

Preliminary analysis of distribution and variation of perennialmonthly mean water masses in the Bohai Sea,the Huanghai Sea and the East China Sea

On the basis of perennial monthly mean temperature and salinity data, the classification of monthly water masses at the surface and the bottom in the Bohai Sea, the Huanghai Sea and the East China Sea, has been made by using the method of fuzzy cluster from the modified characteristic of water masses in the shallow water area. In this paper, the basic features, growth and decline patterns of water masses in relation to fishing grounds in the whole shelves of the Bohai Sea, the Huanghai Sea and the East China Sea are discussed with emphasis.

Analysis of variation in temperature-responsive leaf color mutant lines induced from Gamma irradiation in rice(Oryza sativa L.)

Eight lines of temperature-responsive leaf colormutants induced by applying 300 Gy Gamma-ray irradiation to Thermo-sensitive genic malesterile line 2177s,were obtained through con-tinuous selection in seven generations..Theleaves of these lines started to become greenafter the fourth leaf extension,and except