Utilization of multi‐scale geomorphometric algorithms and third‐order morphometric variables for soil thickness modeling

The nonlinear superharmonic resonance phenomenon of damped circular sandwich plates under uniform load is investigated. From the movement equation of circular sandwich plate showed in displacement components, got the relevant nonlinear vibration equation by Galerkin method. Under the clamped BC. Using multi-scale method, the periodical solutions were obtained which was of nonlinear the third-order superharmonic resonance. The FRF equation of the superharmonic resonance is obtained, and the necessary and sufficient condition on stability of the vibration are obtained synchronously.The infection to the amplitude while the correlative physical and geometric parameters changing were discussed, Drew the trajectories in moving phase planes during the stabilization process, and the stabilities and singularities of the solutions are analyzed.

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Analysis of the phase structure of fluid vibrations with floating longitudinally compressed elastic plate in nonlinear interaction of the surface progressive waves

Vestnik of Saint Petersburg University Applied Mathematics Computer Science Control Processes ◽

10.21638/11701/spbu10.2020.301 ◽

2020 ◽

Vol 16 (3) ◽

pp. 226-237

Author(s):

Anton A. Bukatov ◽

Keyword(s):

Elastic Plate ◽

Plate Thickness ◽

Compressive Force ◽

Finite Amplitude ◽

Harmonic Amplitude ◽

Vertical Acceleration ◽

Third Order ◽

Multi Scale ◽

Wave Disturbances ◽

Vertical Displacements

Based on the asymptotic expansions obtained by the multi-scale method up to the third order of smallness for the potential velocity of liquid particles and the plate-fluid surface elevation, the dispersion properties of the vibrations generated by the interaction of progressive surface wave harmonics of finite amplitude are analyzed in the article. The effect of nonlinearity of acceleration of vertical displacements of an elastic plate on the dispersion characteristics of wave disturbances is studied. The dependence of the vibration frequency is estimated by taking into account the nonlinearity of the first and second approximations values, the plate thickness, and the longitudinal compressive force. It is shown that the sign of the amplitude of the second interacting harmonic and the nonlinearity of the acceleration of vertical displacements of the longitudinally compressed elastic plate affect the vibration phase. It was found that with a decrease in the wavelength of the initial harmonic, the influence of the plate’s nonlinearity vertical acceleration is enhanced. The presence of compressive force is manifested in a decrease in the frequency of vibrations of the wave disturbance in comparison with the frequency obtained in the absence of longitudinal compression, both with a positive and negative sign of the second interacting harmonic amplitude.

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Towards multi-scale fuzzy sparse discriminant analysis using local third-order tensor model of face images

Neurocomputing ◽

10.1016/j.neucom.2015.12.019 ◽

2016 ◽

Vol 185 ◽

pp. 53-63 ◽

Cited By ~ 1

Author(s):

Xiaoning Song ◽

Zhen-Hua Feng ◽

Xibei Yang ◽

Xiaojun Wu ◽

Jingyu Yang

Keyword(s):

Discriminant Analysis ◽

Tensor Model ◽

Third Order ◽

Order Tensor ◽

Multi Scale ◽

Face Images

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High Accuracy Simulation for the Weakly Coupled System of Two Second Order Ordinary Differential Equations

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.467-469.377 ◽

2011 ◽

Vol 467-469 ◽

pp. 377-382

Author(s):

Xin Cai

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Asymptotic Properties ◽

Coupled System ◽

Second Order ◽

Third Order ◽

Multi Scale ◽

Weakly Coupled ◽

Weakly Coupled System ◽

Component Systems

Coupled system of two second order ordinary differential equations with small parameter was considered. This is a multi-scale system. The solution of the system will change rapidly near both sides of the boundary layer. The system was decomposed into several systems in order to have fourth order asymptotic decomposition firstly. The asymptotic properties of all these systems were discussed secondly. The third order numerical methods were constructed for left side and right side singular component systems thirdly. The error estimation for the system was given finally.

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Transforming Analytically Intractable Dynamical Systems with a Control Parameter into a Tractable Ginzburg-Landau Equation: Few Illustrations

The Nepali Mathematical Sciences Report ◽

10.3126/nmsr.v35i1-2.29978 ◽

2018 ◽

Vol 35 (1-2) ◽

pp. 35-44 ◽

Cited By ~ 1

Author(s):

C. Kanchana ◽

P.G. Siddheshwar

Keyword(s):

Dynamical Systems ◽

Control Parameter ◽

Landau Equation ◽

Chen System ◽

Third Order ◽

Ginzburg Landau ◽

First Order ◽

Multi Scale ◽

Ginzburg Landau Equation ◽

Fifth Order

In the paper a means of making a simplified study of dynamical systems with a control parameter is presented. The intractable, third-order classical Lorenz system, the Lorenz-like Chen system and two topologically dissimilar fifth-order Lorenz systems are considered for illustration. Using the multi-scale method, these systems are reduced to an analytically tractable first-order Ginzburg-Landau equation (GLE) in one of the amplitudes. The analytical solution of the GLE is used to find the remaining amplitudes.

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Probe size and 5th-order aberration

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100125609 ◽

1987 ◽

Vol 45 ◽

pp. 134-135 ◽

Cited By ~ 1

Author(s):

Zhifeng Shao

Keyword(s):

Electron Probe ◽

Spherical Aberration ◽

Wave Length ◽

Cylindrical Symmetry ◽

Electron Wave ◽

Third Order ◽

The Third ◽

Probe Radius ◽

Small Probe ◽

Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

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Children’s Recall of Approximations to English

Journal of Speech and Hearing Research ◽

10.1044/jshr.1602.201 ◽

1973 ◽

Vol 16 (2) ◽

pp. 201-212 ◽

Cited By ~ 3

Author(s):

Elizabeth Carrow ◽

Michael Mauldin

Keyword(s):

Language Development ◽

Fourth Order ◽

Third Order ◽

Memory Processes ◽

The Third ◽

General Index ◽

General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

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