A generalized wave action conservative equation for the dissipative dynamical system in the nearshore region

To describe the various complex mechanisms of the dissipative dynamical system between waves, currents, and bottoms in the nearshore region that induce typically the wave motion on large-scale variation of ambient currents, a generalized wave action equation for the dissipative dynamical system in the nearshore region is developed by using the mean-flow equations based on the Navier-Stokes equations of viscous fluid, thus raising two new concepts: the vertical velocity wave action and the dissipative wave action, extending the classical concept, wave action, from the ideal averaged flow conservative system into the real averaged flow dissipative system (that is, the generalized conservative system). It will have more applications.

Chaotic dynamic analysis of viscoelastic plates

The dynamic buckling of viscoelastic plates with large deflection is investigated in this paper by using chaotic and fractal theory. The material behavior is given in terms of the Boltzmann superposition principle. in order to obtain accurate computation results, the nonlinear integro-differential dynamic equation is changed into an autonomic four-dimensional dynamical system. The numerical time integrations of equations are performed by using the fourth-order Runge-Kutta method. And the Lyapunov exponent spectrum, the fractal dimension of strange attractors and the time evolution of deflection are obtained. The influence of geometry nonlinearity and viscoelastic parameter on the dynamic buckling of viscoelastic plates is discussed.

Weibull modulus for diverse strength due to sample-specificity

By sample specificity it is meant that specimens with the same nominal material parameters and tested under the same environmental conditions may exhibit different behavior with diversified strength. Such an effect has been widely observed in the testing of material failure and is usually attributed to the heterogeneity of material at the mesoscopic level. The degree with which mesoscopic heterogeneity affects macroscopic failure is still not clear. Recently, the problem has been examined by making use of statistical ensemble evolution of dynamical system and the mesoscopic stress re-distribution model (SRD). Sample specificity was observed for non-global mean stress field models, such as the duster mean field model, stress concentration at tip of microdamage, etc. Certain heterogeneity of microdamage could be sensitive to particular SRD leading to domino type of coalescence. Such an effect could start from the microdamage heterogeneity and then be magnified to other scale levels. This trans-scale sensitivity is the origin of sample specificity. The sample specificity leads to a failure probability Phi (N) with a transitional region 0 < (N) < 1, so that globally stable and catastrophic modes could co-exist. It is found that the scatter in strength can fit the Weibull distribution very well. Hence, the Weibull modulus is indicative of sample specificity. Numerical results obtained from the SRD for different non-global mean stress fields show that Weibull modulus increases with increasing sample span and influence region of microdamage.

Multiscale Coupling in Complex Mechanical Systems

Multiscale coupling attracts broad interests from mechanics, physics and chemistry to biology. The diversity and coupling of physics at different scales are two essential features of multiscale problems in far-from-equilibrium systems. The two features present fundamental difficulties and are great challenges to multiscale modeling and simulation. The theory of dynamical system and statistical mechanics provide fundamental tools for the multiscale coupling problems. The paper presents some closed multiscale formulations, e.g., the mapping closure approximation, multiscale large-eddy simulation and statistical mesoscopic damage mechanics, for two typical multiscale coupling problems in mechanics, that is, turbulence in fluids and failure in solids. It is pointed that developing a tractable, closed nonequilibrium statistical theory may be an effective approach to deal with the multiscale coupling problems. Some common characteristics of the statistical theory are discussed.

Multiscale Coupling: Challenges and Opportunities

Multiscale coupling is ubiquitous in nature and attracts broad interests of scientists from mathematicians, physicists, machinists, chemists to biologists. However, much less attention has been paid to its intrinsic implication. In this paper, multiscale coupling is introduced by studying two typical examples in classic mechanics: fluid turbulence and solid failure. The nature of multiscale coupling in the two examples lies in their physical diversities and strong coupling over wide-range scales. The theories of dynamical system and statistical mechanics provide fundamental methods for the multiscale coupling problems. The diverse multiscale couplings call for unified approaches and might expedite new concepts, theories and disciplines.

VISUALIZATION RESULTS OF AXISYMMETRICAL WAKE FLOW WITH/WITHOUT ACOUSTIC EXCITATION

Visualization results demonstrate the evolution of Kelvin-Helmholtz unstable waves into vortex pairing in a separated shear layer of a blunf circular. The results with acoustic excitation are quite different from that without acoustic excitation, and the phenomenon with excitation in a separated shear layer follows the rule of Devil s staircase, which always occurs in a non-linear dynamical system of two coupling vibrators.

Symmetry of chaotic attractors and kink-antikink structures in CMLs

In this paper the symmetries of coupled map lattices (CMLs) and their attractors are investigated by group and dynamical system theory, as well as numerical simulation, by means of which the kink-antikink patterns of CMLs in space-amplitude plots are discussed.

陡坡带砂砾岩体油气成藏模式研究——以东营凹陷西北部陡坡带为例

Based on the study of sequence stratigraphy, modern sedimentary, basin analysis, and petroleum system in abrupt slop of depression, this paper builds sedimentary system and model, sandy bodies distribution, and pool-forming mechanism of subtle trap. There are some conclusions and views as follows. By a lot of well logging and seismic analysis, the author founded up the sequence stratigraphic of the abrupt slope, systematically illustrated the abrupt slope constructive framework, and pointed out that there was a special characteristics which was that south-north could be divided to several fault block and east-west could be carved up groove and the bridge in studying area. Based all these, the author divided the studying area to 3 fault block zone in which because of the groove became the basement rock channel down which ancient rivers breathed into the lake, the alluvial fan or fan delta were formed. In the paper, the author illustrated the depositional system and depositional model of abrupt slope zone, and distinguished 16 kinds of lithofacies and 3 kinds of depositional systems which were the alluvial fan and fan-delta system, lake system and the turbidite fan or turbidity current deposition. It is first time to expound completely the genetic pattern and distributing rule of the abrupt slope sandy-conglomeratic fan bodies. The abrupt slope sandy-conglomeratic fan bodies distribute around the heaves showing itself circularity shape. In studying area, the sandy-conglomeratic fan bodies mainly distribute up the southern slope of Binxian heave and Chenjiazhuang heave. There mainly are these sandy-conglomeratic fan body colony which distributes at a wide rage including the alluvial fan, sub-water fluvial and the turbidite fan or the other turbidity current deposition in the I fault block of the Wangzhuang area. In the II fault block there are fan-delta front and sub-water fluvial. And in the Binnan area, there mainly are those the alluvial fan (down the basement rock channel) and the sandy-conglomeratic fan body which formed as narrowband sub-water fluvial (the position of bridge of a nose) in the I fault block, the fan-delta front sandy-conglomeratic fan body in the H fault block and the fan-delta front and the turbidity current deposition sandy-conglomeratic fan body in the m fault block. Based on the reservoir outstanding characteristics of complex classic composition and the low texture maturity, the author comparted the reservoir micro-structure of the Sha-III and Sha-IV member to 4 types including the viscous crude cementation type, the pad cementation type, the calcite pore-funds type and the complex filling type, and hereby synthetically evaluated 4 types sandy- conglomeratic fan body reservoir. In the west-north abrupt slope zone of Dongying Depression, the crude oil source is belonging to the Sha-III and Sha-IV member, the deep oil of Lijin oilfield respectively come from the Sha-III and Sha-IV member, which belongs to the autogeny and original deposition type; and the more crude oil producing by Sha-IV member was migrated to the Wangzhuan area and Zhengjia area. The crude oil of Binnan oil-field and Shanjiasi oil-field belongs to mixed genetic. It is the first time to illustrate systematically the genetic of the viscous crude that largely being in the studying area, which are that the dissipation of the light component after pool-forming, the biological gradation action and the bath-oxidation action, these oil accumulation belonging to the secondary viscous crude accumulation. It is also the first time to compart the studying area to 5 pool-forming dynamical system that have the characteristic including the common pressure and abnormal pressure system, the self-fountain and other-fountain system and the closing and half-closing system etc. The 5 dynamical systems reciprocally interconnected via the disappearance or merger of the Ethology and the fluid pressure compartment zone, the fault and the unconformity surface, hereby formed duplicated pattern oil-gas collecting zone. Three oil-gas pool-forming pattern were founded, which included the self-fountain side-direction migrated collecting pattern, the self-fountain side-direction ladder-shape pool-forming pattern and the other-fountain pressure releasing zone migrated collecting pattern. A series of systemic sandy-conglomeratic fan bodies oil-gas predicting theory and method was founded, based on the groove-fan corresponding relation to confirm the favorable aim area, according as the characteristic of seismic-facies to identify qualitatively the sandy-conglomeratic fan bodies or its scale, used the temporal and frequency analysis technique to score the interior structure of the sandy- conglomeratic fan bodies, applied for coherent-data system analysis technology to describe the boundary of the sandy-conglomeratic fan bodies, and utilized the well logging restriction inversion technique to trace quantificational and forecast the sandy-conglomeratic fan bodies. Applied this technique, totally 15 beneficial sandy-conglomeratic fan bodies were predicted, in studying area the exploration was preferably guided, and the larger economic benefit and social benefit was acquired.

高斯束射线追踪

Using the approximate high-frequency asymptotic methods to solve the scalar wave equation, we can get the eikonal equation and transport equation. Solving the eikonal equation by the method of characteristics provides a mathematical derivation of ray tracing equations. So, the ray tracing system is folly based on the approximate high-frequency asymptotic methods. If the eikonal is complex, more strictly, the eikonal is real value at the rays and complex outside rays, we can derive the Gaussian beam. This article mainly concentrates on the theory of Gaussian beam. To classical ray tracing theory, the Gaussina beam method (GBM) has many advantages. First, rays are no longer required to stop at the exact position of the receivers; thus time-consuming two-point ray tracing can be avoided. Second, the GBM yields stable results in regions of the wavefield where the standard ray theory fails (e.g., caustics, shadows zones and critical distance). Third, unlike seismograms computed by conventional ray tracing techniques, the GBM synthetic data are less influenced by minor details in the model representation. Here, I realize kinematical and dynamical system, and based on this, realize the GBM. Also, I give some mathematical examples. From these examples, we can find the importance and feasibility of the ray tracing system. Besides, I've studied about the reflection coefficient of inhomogeneous S-electromagnetic wave at the interface of conductive media. Basing on the difference of directions of phase shift constant and attenuation constant when the electromagnetic wave propagates in conductive medium, and using the boundary conditions of electromagnetic wave at the interface of conductive media, we derive the reflection coefficient of inhomogeneous S-electromagnetic wave, and draw the curves of it. The curves show that the quasi total reflection will occur when the electromagnetic wave incident from the medium with greater conductivity to the medium with smaller conductivity. There are two peak, values at the points of the critical angles of phase shift constant and attenuation constant, and the reflection coefficient is smaller than 1. This conclusion is different from that of total reflection light obviously.

Heteroclinic cycles in lattice dynamical systems

A criterion of spatial chaos occurring in lattice dynamical systems-heteroclinic cycle-is discussed. It is proved that if the system has asymptotically stable heteroclinic cycle, then it has asymptotically stable homoclinic point which implies spatial chaos.

Dynamical symmetry of screened Coulomb potential and isotropic harmonic oscillator

It is shown that for the screened Coulomb potential and isotropic harmonic oscillator, there exists an infinite number of closed orbits for suitable angular momentum values. At the aphelion (perihelion) points of classical orbits, an extended Runge-Lenz vector for the screened Coulomb potential and an extended quadrupole tensor for the screened isotropic harmonic oscillator are still conserved. For the screened two-dimensional (2D) Coulomb potential and isotropic harmonic oscillator, the dynamical symmetries SO3 and SU(2) are still preserved at the aphelion (perihelion) points of classical orbits, respectively. For the screened 3D Coulomb potential, the dynamical symmetry SO4 is also preserved at the aphelion (perihelion) points of classical orbits. But for the screened 3D isotropic harmonic oscillator, the dynamical symmetry SU(2) is only preserved at the aphelion (perihelion) points of classical orbits in the eigencoordinate system. For the screened Coulomb potential and isotropic harmonic oscillator, only the energy (but not angular momentum) raising and lowering operators can be constructed from a factorization of the radial Schrodinger equation.

An adaptive controller for a class of nonlinear system using direction basis function

For a class of nonlinear dynamical systems, the adaptive controllers are investigated using direction basis function (DBF) in this paper. Based on the criterion of Lyapunov' stability, DBF is designed which guarantees that the output of the controlled system asymptotically tracks the reference signals. Finally, the simulation shows the good tracking effectiveness of the adaptive controller.

The many-particle scattering system He++ on He: Experiment and a complete unified description

Highly differential experimental results of the scattering system He++ on He at 30 keV are presented as well as a complete unified theoretical description where excitation, transfer and ionization are treated simultaneously on an ab initio level. The agreement even for highly differential cross sections is nearly complete although no explicit correlation besides Pauli correlation is included in the calculations.