Estimating Heat Fluxes by Merging Profile Formulae and the Energy Budget with a Variational Technique

A variational technique (VT) is applied to estimate surface sensible and latent heat fluxes based on observations of air temperature, wind speed, and humidity, respectively, at three heights (1 m, 4 m, and 10 m), and the surface energy and radiation budgets by the surface energy and radiation system (SERBS). The method fully uses all information provided by the measurements of air temperature, wind, and humidity profiles, the surface energy budget, and the similarity profile formulae as well. Data collected at Feixi experiment station installed by the China Heavy Rain Experiment and Study (HeRES) Program are used to test the method. Results show that the proposed technique can overcome the well-known unstablility problem that occurs when the Bowen method becomes singular; in comparison with the profile method, it reduces both the sensitivities of latent heat fluxes to observational errors in humidity and those of sensible heat fluxes to observational errors in temperature, while the estimated heat fluxes approximately satisfy the surface energy budget. Therefore, the variational technique is more reliable and stable than the two conventional methods in estimating surface sensible and latent heat fluxes.

Optimal estimation of zonal velocity and transport through Luzon Strait using variational data assimilation technique

A P-vector method was optimized using variational data assimilation technique, with which the vertical structures and seasonal variations of zonal velocities and transports were investigated. The results showed that westward and eastward flowes occur in the Luzon Strait in the same period in a year. However the net volume transport is westward. In the upper level (0m -500m),the westward flow exits in the middle and south of the Luzon Strait, and the eastward flow exits in the north. There are two centers of westward flow and one center of eastward flow. In the middle of the Luzon Strait, westward and eastward flowes appear alternately in vertical direction. The westward flow strengthens in winter and weakens in summer. The net volume transport is strong in winter (5.53 Sv) but weak in summer (0.29 Sv). Except in summer, the volume transport in the upper level accounts for more than half of the total volume transport (0m bottom). In summer, the net volume transport in the upper level is eastward (1.01 Sv), but westward underneath.

Optimal estimation of absolute geostrophic velocity field in vicinity of the Luzon Strait using variational data assimilation technique

A P - vector method is optimized using the variational data assimilation technique(VDAT). The absolute geostrophic velocity fields in the vicinity of the Luzon Strait (LS) are calculated, the spatial structures and seasonal variations of the absolute geostrophic velocity field are investigated. Our results show that the Kuroshio enters the South China Sea (SCS) in the south and middle of the Luzon Strait and flows out in the north, so the Kuroshio makes a slight clockwise curve in the Luzon Strait, and the curve is strong in winter and weak in summer. During the winter, a westward current appears in the surface, and locates at the west of the Luzon Strait. It is the north part of a cyclonic gyre which exits in the northeast of the SCS; an anti-cyclonic gyre occurs on the intermediate level, and it exits in the northeast of the SCS, and an eastward current exits in the southeast of the anti-cyclonic gyre.

SOME GENERAL THEOREMS AND GENERALIZED AND PIECEWISE GENERALIZED VARIATIONAL PRINCIPLES FOR LINEAR ELASTODYNAMICS

From the concept of four-dimensional space and under the four kinds of time limit conditions, some general theorems for elastodynamics are developed, such as the principle of possible work action, the virtual displacement principle, the virtual stress-momentum principle, the reciprocal theorems and the related theorems of time terminal conditions derived from it. The variational principles of potential energy action and complementary energy action, the H-W principles, the H-R principles and the constitutive variational principles for elastodynamics are obtained. Hamilton's principle, Toupin's work and the formulations of Ref. [5], [17]-[24] may be regarded as some special cases of the general principles given in the paper. By considering three cases: piecewise space-time domain, piecewise space domain, piecewise time domain, the piecewise variational principles including the potential, the complementary and the mixed energy action fashions are given. Finally, the general formulation of piecewise variational principles is derived. If the time dimension is not considered, the formulations obtained in the paper will become the corresponding ones for elastostatics.

ELASTIC DYNAMICS VARIATIONAL PRINCIPLE FOR NONLINEAR ELASTIC BODY

Based on paper, the variational principle and generalized variational principle of elastic dynamics for elastic body with nonlinear stress-strain relations are introduced in this paper. The generalized instantaneous variational principle is also raised for the mixed harmonious displacement element and the mixed harmonious stress element.

RATED GENERALIZED SUB-REGION VARIATIONAL PRINCIPLES IN NONLINEAR ELAS TODYNAMICS

In this paper, the rated generalized sub-region mixed and hybrid variational principles in nonlinear elastodynamics were constructed on the basis of Co-Moving coordinate description and S-R decomposition theorem which contain five independent arguments, that are the velocity gradient, momentum, velocity, stress and strain rate.

EXISTENCE AND ALGORITHM OF SOLUTIONS FOR GENERAL MULTIVALUED MIXED IMPLICIT QUASI-VARIATIONAL INEQUALITIES

A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case , introduced and studied by Ding Xie-ping . The auxiliary variational principle technique was applied to solve this class of general multivalued mixed implicit quasi-variational inequalities. Firstly, a new auxiliary variational inequality with a proper convex , lower semicontinuous , binary functional was defined and a suitable functional was chosen so that its unique minimum point is equivalent to the solution of such an auxiliary variational inequality . Secondly , this auxiliary variational inequality was utilized to construct a new iterative algorithm for computing approximate solutions to general multivalued mixed implicit quasi-variational inequalities . Here , the equivalence guarantees that the algorithm can generate a sequence of approximate solutions. Finally, the existence of solutions and convergence of approximate solutions for general multivalued mixed implicit quasi-variational inequalities are proved. Moreover, the new convergerce criteria for the algorithm were provided. Therefore, the results give an affirmative answer to the open question raised by M. A . Noor, and extend and improve the earlier and recent results for various variational inequalities and complementarity problems including the corresponding results for mixed variational inequalities, mixed quasi-variational inequalities and quasi-complementarity problems involving the single-valued and set- valued mappings in the recent literature .

NONLINEAR BENDING OF SIMPLY SUPPORTED RECTANGULAR SANDWICH PLATES

The fundamental equations and boundary conditions of the nonlinear bending theory for a rectangular sandwich plate with a soft core were derived by using the method of calculus of variations. Then the nonlinear bending for a simply supported rectangular sandwich plate under the uniform lateral load was investigated by using the perturbation method. As a result, a quite accurate analytic solution was obtained.

NONLINEAR GALERKIN METHOD FOR THE EXTERIORNONSTATIONARY NAVIER-STOKES EQUATIONS

A new algorithm combining nonlinear Galerkin method and coupling method of finite element and boundary element is introduced to solve the exterior nonstationary Navier-Stokes equations. The regularity of the coupling variational formulation and the convergence of the approximate solution corresponding to the algorithm are proved. If the fine mesh h is chosen as coarse mesh H-square, the nonlinear Galerkin method, nonlinearity is only treated on the coarse grid and linearity is treated on the fine grid. Hence, the new algorithm can save a large amount of computational time.

Hybrid Element Method for Calculation of Harbor Resonance

This paper presents a hybrid element method for calculating harbor resonance in a coastal or offshore harbor under the effects of friction and boundary absorption. The friction term is assumed to be proportional to the flow velocity with a phase difference. The boundary absorption adopts a condition similar to the impedance condition in acoustics. In the near region a variational principle is established. In the far region the solution satisfies the Helmholtz equation. Computation of results of harbor resonance by the model show good agreement between experimental data and theoretical results.

PARAMETRIC QUADRATIC PROGRAMMING METHOD FOR VISCOPLASTICITY

Perzyna model in viscoplasticity has been studied by the parametric variational principle, which could be transformed into solving the parametric quadratic programming problem. The FEM form of this problem and its implementation have also been discussed in the paper.

ON SOME IMPORTANT PROBLEMS IN ANALYTICAL DYNAMICS OF NON-HOLONOMIC SYSTEMS

By using deductive method, Chetaev condition was derived in this paper. The authors pointed out that the viewpoint is a misunderstanding which considers that the processes of variation and differentiation are not permutable in non-holonomic dynamics. Two classical relations of non-holonomic systems were first put forward in this paper, and their introduction will bring benefit for the application of integral variational principle in nonholonomic systems.

LAGRANGE EQUATION OF A CLASS OF NONHOLONOMIC SYSTEMS

Making use of conclusions from [1]: (1) d-δ operations are commutative; (2) the Appell-Chetaev condition restricting virtual displacements is superfluous, the present paper derives the Lagrange equation without multipliers for a class of first-order nonlinear nonholonomic dynamical systems by means of variational principle. This kind of equations is new.

ON BUCKLING OF CANTILEVER RECTANGULAR PLATES UNDER SYMMETRICAL EDGE LOADING

The stability of cantilever rectangular plates under the symmetrical edge loading will be studied in this paper by the variational calculus. The minimum critical loading is determined for cantilever rectangular plates subjected to various edge loadings symmetrically on a pair of opposite free edges. We'll discuss the least critical loadings when the buckling of rectangular plates acted on by a pair of concentrated forces, uniformly distributed loads, locally uniform distributed loads, distributed loads in the form of triangle and a pair of concentrated couples occur respectively.

ASYMPTOTIC SOLUTIONS OF MATHIEU EQUATION WITH DAMPING

This paper first reduces the motion equation of a collapsible tube to the Mathieu equation with damping. Then the stability charts correcting the accuracy to each order are obtained with the method of asymptotic expansions. The accuracy of the results obtained with the average variational method is shown. And some phenomena observed in the experiment are also explained.

DEGENERATE PARABOLIC EQUATION AND UNILATERALCONSTRAINT SYSTEMS

The existence and regularity of solution to a nonlinear and nonautonomous multivalued parabolic equation were discussed. The equation represents some energy-dissipative problems with nonlinear constitutive constraints and non-differential external constraints in physics, mechanics and optimization.

Study on the Variational Assimilation Technique for the Retrieval of Wind Fields from Doppler Radar Data

This paper introduces a variational assimilation technique for the retrieval of wind fields from Doppler radar data. The assimilated information included both the radial velocity （RV） and the movement of radar echo. In this assimilation technique, the key is transforming the movement of radar echo to a new radar measuring variable- ＂apparent velocity＂ （AV）. Thus, the information of wind is added, and the indeterminacy of recovering two-dimensional wind only by AV was overcome effectively by combining RV with AV. By means of CMA GRAPES-3Dvar and CINRAD data, some experiments were performed. The results show that the method of retrieval of wind fields is useful in obtaining the construction of the weather system.

Estimation of Transverse Thermal Conductivity of Doubly-periodic Fiber Reinforced Composites

For steady-state heat conduction,a new variational functional for a unit cell of composites with periodic microstructures is constructed by considering the quasi-periodicity of the temperature field and in the periodicity of the heat flux fields. Then by combining with the eigenfunction expansion of complex potential which satisfies the fiber-matrix interface conditions, an eigenfunction expansion-variational method （EEVM）based on a unit cell is developed. The effective transverse thermal conductivities of doubly-periodic fiber reinforced composites are calculated, and the first-order approximation formula for the square and hexagonal arrays is presented, which is convenient for engineering application. The numerical results show a good convergency of the presented method,even though the fiber volume fraction is relatively high. Comparisons with the existing analytical and experimental results are made to demonstrate the accuracy and validity of the first-order approximation formula for the hexagonal array.

Collision-induced timing jitter in dispersion-managed WDM soliton system with filtering

Taking into account the randomicity of collision positions and the arbitrary encoding of data in channel, the influences of different dispersion management on collision-induced timing jitter in a filtered wavelength division multiplexing (WDM) soliton system are obtained statistically and numerically by applying a set of coupled ordinary differential equations which are derived through variational procedure. The optimal dispersion managements which can greatly reduce the collision-induced timing jitter are found. The multi-channel collision-induced timing jitters in a filtered WDM soliton system are given with an optimal dispersion management and constant dispersion.