A UNIFIED ENERGY APPROACH TO A CLASS OF MICROMECHANICS MODELS FOR MICROCRACKED SOLIDS

Micromechanics models have been developed For the determination of the elastic moduli of microcracked solids based on different approaches and interpretations, including the dilute or non-interacting solution, the Mori-Tanaka method, the self-consistent method, and the generalized self-consistent method. It is shown in the present study that all these micromechanics models can be unified within an energy-equivalence framework, and that they differ only in the way in which the microcrack opening and sliding displacements are evaluated. Relevance to the differential methods and the verification of these models are discussed.

Gravity field recovery from GOCE orbits using the energy conservation approach

The sum of the dissipative energy and energy constant of the GOCE satellite is found by a priori gravity field model at first, and the GOCE dissipative energy is obtained by computing the adjacent epoch difference via the differential method. Then, a gravity field model GOCE-ECPO1, which up to the degree and order 80, is recovered by the energy conservation approach from the 103-day precise orbital data of the GOCE satellite collected from November 1, 2009 to January 12, 2010. Finally, the model is compared with existing models EGM96, ITG-CHAMP05S, EIGEN-GRACE2010S, EIGEN-6C and GO CONS GCF 2 DIR_R3. The results show that at the same order and degree, the accuracy of model GOCE-EBPO1 is higher than those of models EGM96 and ITG-CHAMP05S, but lower than those of models EIGEN-GRACE2010S, EIGEN-6C and GO_CONS_GCF 2 DIR_R3, which is mainly caused by the pole gap.

Planck’s Oscillators at Low Temperatures and Haken’s Perturbation Approach to the Quantum Oscillators Reconsidered

In the first step the extremal values of the vibrational specific heat and entropy represented by the Planck oscillators at the low temperatures could be calculated. The positions of the extrema are defined by the dimensionless ratios between the quanta of the vibrational energy and products of the actual temperature multiplied by the Boltzmann constant. It became evident that position of a local maximum obtained for the Planck’s average energy of a vibration mode and position of a local maximum of entropy are the same. In the next step the Haken’s time-dependent perturbation approach to the pair of quantum non-degenerate Schr?dinger eigenstates of energy is re-examined. An averaging process done on the time variable leads to a very simple formula for the coefficients entering the perturbation terms.

Analysis of Dynamic Stability of Ocean Gravity Structure Foundations

Based on unified equivalent harmonic loading on seabed foundation and energy approach suggested by the authors, the development of dynamic pore water pressure and stability of soil foundation for the vibration of ocean gravity structures excited by random wave loading are analysed. It may be seen that the present method for the study of dynamic problems of ocean gravity structure soil foundations is more reasonable and convenient.

Transient-Spatial Pattern Mining of Eddy Current Pulsed Thermography Using Wavelet Transform

Eddy current pulsed thermography（ECPT） is an emerging Non-destructive testing and evaluation（NDT E） technique, which uses hybrid eddy current and thermography NDT E techniques that enhances the detectability from their compensation. Currently, this technique is limited by the manual selection of proper contrast frames and the issue of improving the efficiency of defect detection of complex structure samples remains a challenge. In order to select a specific frame from transient thermal image sequences to maximize the contrast of thermal variation and defect pattern from complex structure samples, an energy driven approach to compute the coefficient energy of wavelet transform is proposed which has the potential of automatically selecting both optimal transient frame and spatial scale for defect detection using ECPT. According to analysis of the variation of different frequency component and the comparison study of the detection performance of different scale and wavelets, the frame at the end of heating phase is automatically selected as an optimal transient frame for defect detection. In addition, the detection capabilities of the complex structure samples can be enhanced through proper spatial scale and wavelet selection. The proposed method has successfully been applied to low speed impact damage detection of carbon fibre reinforced polymer（CFRP） composite as well as providing the guidance to improve the detectability of ECPT technique.

Semi-Implicit Spectral Deferred Correction Method Based on the Invariant Energy Quadratization Approach for Phase Field Problems

This paper presents a high order time discretization method by combining the semi-implicit spectral deferred correction method with energy stable linear schemes to simulate a series of phase field problems.We start with the linear scheme,which is based on the invariant energy quadratization approach and is proved to be linear unconditionally energy stable.The scheme also takes advantage of avoiding nonlinear iteration and the restriction of time step to guarantee the nonlinear system uniquely solvable.Moreover,the scheme leads to linear algebraic system to solve at each iteration,and we employ the multigrid solver to solve it efficiently.Numerical re-sults are given to illustrate that the combination of local discontinuous Galerkin(LDG)spatial discretization and the high order temporal scheme is a practical,accurate and efficient simulation tool when solving phase field problems.Namely,we can obtain high order accuracy in both time and space by solving some simple linear algebraic equations.

Two topological approaches to resonance energy and the relation between them

Two of the present authors recently put forward a novel approach to resonance energy which is based on a similar topological reasoning as a previously elaborated resonance energy concept. It is shown that these two approaches are not completely equivalent. Several other properties of the new resonance energy are pointed out.

Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei: systematic investigation of the triaxiality effect on the fission barrier

Static fission barriers for 95 even-even transuranium nuclei with charge number Z = 94-118 have been systematically investigated by means of pairing self-consistent Woods-Saxon-Strutinsky calculations using the potential energy surface approach in multidimensional（β;, γ, β;） deformation space. Taking the heavier （252）;f nucleus（with the available fission barrier from experiment） as an example, the formation of the fission barrier and the influence of macroscopic, shell and pairing correction energies on it are analyzed. The results of the present calculated β;values and barrier heights are compared with previous calculations and available experiments. The role of triaxiality in the region of the first saddle is discussed. It is found that the second fission barrier is also considerably affected by the triaxial deformation degree of freedom in some nuclei（e.g., the Z =112-118 isotopes）. Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths as a function of the nucleon numbers are investigated. In addition, the effects of Woods-Saxon potential parameter modifications（e.g.,the strength of the spin-orbit coupling and the nuclear surface diffuseness） on the fission barrier are briefly discussed.

Pendulum waves and basics of «geomechanical thermodynamics»

It is shown that modern achievements in the field of experimental and theoretical researches and developments of innovative measuring systems for monitoring of non-linear dynamic and kinematic characteristics allow to formulate basics of new academic discipline,designated as“geomechanical thermodynamics”.The following circumstances can be considered as the most important prerequisites for development of this new discipline.(1)Practical completeness of the classical thermodynamics,based on kinetic gas theory and molecular movements in solid bodies;(2)Creation of“formular construction tool”for the description of dynamic and kinematic characteristics of pendulum waves and energy conditions of their occurrence and propagation from dynamic sources,located in multi-phased stressed rock mass and geomaterials with block-hierarchical structure;(3)Principal opportunity to establish formal relations between substantial energy carriers of“packages”of nonlinear pendulum waves(geoblocks of certain hierarchical levels according to their diameters)and“molecules”:their movement,velocity and acceleration of the“molecules”↔“geoblock”;“force interactions between molecules”↔“non-linear elastic interaction between geoblocks”,etc.The term of“geomechanical temperature”is introduced and its analytical expression,which is proportional to kinetic energy of movement of geoblocks with defined volume for their hierarchical subsequence at“confined”conditions of the stressed rock mass,is shown.The similar aspects are discussed,when emission acousticelectromagnetic fields are fixed using corresponding coefficients of mechanical-electrical and mechanicalacoustic transformations.In order to quantitively describe the evolution of energy state of local zones of stressstrain concentration and surroundings of their non-linear influence from catastrophic events at the natural and mine-engineering systems(earthquakes,rock bursts,etc.),the terms of their geomechanical and thermodynamic stages are introduced and specified:Tiei 20;t;;;*T‒with background states ei 20;*T and three major stages ei2t;;T outlined,where(t)is the concentration,(,‒)are the failure and relaxation and(*)is the quasirecovering up to“background”level after the occurred catastrophic event.Using certain examples,the existence of critical elastic energy content of local zones with“meta-stable state”,which is transforming to quasiresonance process of failure and relaxation of“excessive”energy,is shown eTT.