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.

TECHNICAL STABILITY OF NONLINEAR TIME-VARYING SYSTEMS WITH SMALL PARAMETERS

Technical stability:allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered. Based on a differential comparison principle and a basic monotonicity condition, technical stability relative to certain prescribed state constraint sets of a class of nonlinear time-varying systems with small parameters was analyzed by means of vector Liapunov function method. Explicit criteria of technical stability are established in terms of coefficients of the system under consideration. Conditions under which the technical stability of the system can be derived from its reduced linear time-varying (LTV) system were further examined, as well as a condition for linearization approach to technical stability of general nonlinear systems. Also, a simple algebraic condition of exponential asymptotic stability of LTV systems is presented. Two illustrative examples are given to demonstrate the availability of the presently proposed method.

Comparative Methodical Assessment of Established MOSFET Threshold Voltage Extraction Methods at 10-nm Technology Node

Threshold voltage (VTH) is the most evocative aspect of MOSFET operation. It is the crucial device constraint to model on-off transition characteristics. Precise VTH value of the device is extracted and evaluated by several estimation techniques. However, these assessed values of VTH diverge from the exact values due to various short channel effects (SCEs) and non-idealities present in the device. Numerous prevalent VTH extraction methods are discussed. All the results are verified by extensive 2-D TCAD simulation and confirmed through analytical results at 10-nm technology node. Aim of this research paper is to explore and present a comparative study of largely applied threshold extraction methods for bulk driven nano-MOSFETs especially at 10-nm technology node along with various sub 45-nm technology nodes. Application of the threshold extraction methods to implement noise analysis is briefly presented to infer the most appropriate extraction method at nanometer technology nodes.

Simultaneous inversion of velocity distribution and interface positions

This paper deals with the simultaneous inversion of velocity distribution and interface positions in a laterally heterogeneous medium using seismic travel time data. Due to the application of variable step length and linear interpolation techniques (for both theoretical travel times and the partial derivative matrix), the computing speed is increased greatly. As compared with other domestic computing programs of this kind, it is five times or more faster than others. Besides reflected waves, the transmitted waves can also be used to form the partial derivative matrix of travel times with respect to interface positions. So this method can make full use of the information about interface positions contained in various transmitted waves and speed up the convergence rate. Digital tests and processing results of real data indicate the feasibility and effectiveness of the method and its program.

Correlation of Critical Micelle Concentration of Sodium Alkyl Benzenesulfonates with MolecularDescriptors

The hydrophobic-hydrophilic segment geometries of 36 sodium alkyl benzenesulfonates were fully optimized and calculated by abinitio RHF/6-31G（d）, quantum chemical data such as the charge density, the energy of molecular orbital and the dipole moment were obtained. Based on two topological descriptors and one quantum chemical descriptor, a significant quantitative structure-property relationship （QSPR） model for the critical micelle concentration （Cmc） of sodium alkyl benzenesulfonate surfactants was obtained by using the multiple linear regression technique. The good correlation coefficient of Re （0. 980） and cross-validation correlation coefficient Rcv^2 （0. 974） indicate the excellent capability and stability of the regression equation developed. In addition, linear relationships between logarithm of Cmc and the dipole moment of surfaetant hydrophobic hydrophilic segments for each homologous series have also been established with high correlation coefficient.

On the Measurement of Lower Solution Bounds of the Discrete Algebraic Lyapunov Equation

In this paper, estimations of the lower solution bounds for the discrete algebraic Lyapunov Equation (the DALE) are addressed. By utilizing linear algebraic techniques, several new lower solution bounds of the DALE are presented. We also propose numerical algorithms to develop sharper solution bounds. The obtained bounds can give a supplement to those appeared in the literature.

Review of Dimension Reduction Methods

Purpose: This study sought to review the characteristics, strengths, weaknesses variants, applications areas and data types applied on the various Dimension Reduction techniques. Methodology: The most commonly used databases employed to search for the papers were ScienceDirect, Scopus, Google Scholar, IEEE Xplore and Mendeley. An integrative review was used for the study where 341 papers were reviewed. Results: The linear techniques considered were Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Singular Value Decomposition (SVD), Latent Semantic Analysis (LSA), Locality Preserving Projections (LPP), Independent Component Analysis (ICA) and Project Pursuit (PP). The non-linear techniques which were developed to work with applications that have complex non-linear structures considered were Kernel Principal Component Analysis (KPCA), Multi-dimensional Scaling (MDS), Isomap, Locally Linear Embedding (LLE), Self-Organizing Map (SOM), Latent Vector Quantization (LVQ), t-Stochastic neighbor embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP). DR techniques can further be categorized into supervised, unsupervised and more recently semi-supervised learning methods. The supervised versions are the LDA and LVQ. All the other techniques are unsupervised. Supervised variants of PCA, LPP, KPCA and MDS have been developed. Supervised and semi-supervised variants of PP and t-SNE have also been developed and a semi supervised version of the LDA has been developed. Conclusion: The various application areas, strengths, weaknesses and variants of the DR techniques were explored. The different data types that have been applied on the various DR techniques were also explored.

Orbital maneuver strategy design based on piecewise linear optimization for spacecraft soft landing on irregular asteroids

Recently,asteroid exploration becomes an important branch of human’s deep space activities.In this paper,a piecewise linear optimal orbital maneuver strategy is designed for a spacecraft soft landing on irregular-shaped asteroids.First,the space around an irregular asteroid is converted into several grid units,and the gravitational field of the asteroid is linearly fitted in each unit.Then,the soft-landing orbital maneuver strategy design problem is formulated as a piecewise linear optimal problem,and further transferred into a family of two-point boundary value problems,which can be solved using collocation method.Finally,a corresponding algorithm is developed to obtain the piecewise linear optimal maneuver strategy,which is proved to be able to achieve the soft-landing mission well.Simulation results show that the error of the model linearization is small enough,while the calculation efficiency is remarkably improved,and the robustness of maneuver strategy is also improved.

STREAMLINE-EQUIVORTICITY-LINE ITERATION METHOD FOR CALCULATING STEADY FLOW OF NONUNIFORM STREAM PAST A CIRCULAR CYLINDER

In this paper, an iteration method is presented to calculate the steady noseparation flow past a circular cylinder with brokenline-shaped velocity profile. At each iteration step, the streamlines of the last step are considered as equivorticity lines to determine the new flow field. The iterative process is stopped when certain convergence criterion is reached. Several examples are given which show the effectiveness of the method.

Analytical study of friction coefficients of pomegranate seed as essential parameters in design of post-harvest equipment

Friction coefficients(static friction coefficient(SFC)and dynamic friction coefficient(DFC))of pomegranate seed on different structural surfaces(glass,aluminum,plywood,galvanized steel and rubber)as affected by moisture content(4-21.9%(d.b.))and sliding velocity(1.4-16(cm/s))were investigated.Analysis of variance(ANOVA)was performed to determine the effect of main treatments and their interactions on SFC and DFC.Significance of single or multiple effect of the main treatments with five levels was assessed using Duncan’s multiple range test(DMRT).To predict SFC and DFC,multiple linear regression(MLR)modeling technique was applied for each type of structural surface.The goodness of fit of each MLR model was evaluated using statistical parameters:coefficient of determination,root mean square error and mean relative deviation modulus.Results showed that the minimum and maximum SFC or DFC were in minimum and maximum moisture content on glass and rubber surface,respectively.ANOVA table indicated the significant effect of main treatments and their interactions on SFC and DFC at significance level of 1%(P<0.01).According to DMRT results,SFC linearly increased as moisture content increased and DFC increased also linearly as individual or simultaneous increment of moisture content and sliding velocity occurred,for all experimental conditions.According to the obtained statistical parameters,both SFC and DFC were properly predicted by means of MLR modeling technique.

Quadratic mean-field reflected BSDEs

In this paper,we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in the second unknown z.Using a linearization technique and the BMO martingale theory,we first apply a fixed-point argument to establish the uniqueness and existence result for the case with bounded terminal condition and obstacle.Then,with the help of theθ-method,we develop a successive approximation procedure to remove the boundedness condition on the terminal condition and obstacle when the generator is concave(or convex)with respect to the second unknown.

Review of General Modeling Approaches of Power Converters

The modeling approaches of power converters occupy an important position in power electronic systems and have made considerable progress over the past years.Continuous modeling approaches and linearization techniques are reviewed,including the state-space average model,generalized average model,averaged small-signal model,and describing function method.A Buck converter with PWM modulation and voltage-mode control is taken as an example to compare the advantages and disadvantages of different methods through simulation analysis.Moreover,the corresponding equivalent circuit with an intuitive physical meaning of state-space average model,generalized average model,and averaged small-signal model is given.The results point out that the generalized average model can improve the modeling accuracy based on the state-space average model.In the linearization techniques,the averaged small-signal model reflects accuracy at low frequencies,but introduces phase lag in the high-frequency region.The describing function method is derived from harmonic linearization,which takes into account the sideband effect and improves the modeling accuracy at high frequencies.