Statistical Properties of Spatial Derivatives of the Amplitude and Intensity of Monochromatic Speckle Patterns

1979 ◽  
Vol 26 (12) ◽  
pp. 1505-1521 ◽  
Author(s):  
K.J. Ebeling
Keyword(s):  
Statistical Properties ◽  
Speckle Patterns ◽  
Spatial Derivatives ◽  
Derivatives Of

Vibration attenuation of a two-link flexible arm carried by a translational stage

2018 ◽  
Vol 24 (23) ◽  
pp. 5650-5664 ◽  
Author(s):  
Shang–Teh Wu ◽  
Shan-Qun Tang ◽  
Kuan–Po Huang
Keyword(s):  
Feedback Loop ◽  
Control Method ◽  
Flexible Manipulator ◽  
Closed Loop System ◽  
Flexible Arm ◽  
Vibration Attenuation ◽  
Shaft Encoder ◽  
High Frequency Vibrations ◽  
Spatial Derivatives ◽  
Derivatives Of

This paper investigates the vibration control of a two-link flexible manipulator carried by a translational stage. The first and the second links are each driven by a stage motor and a joint motor. By treating the joint motor as a virtual spring, the two-link manipulator can be regarded as an integral flexible arm driven by the stage motor. A noncollocated controller is devised based on feedback from the deflection of the virtual spring, which can be measured by a shaft encoder. Stability of the closed-loop system is analyzed by examining the spatial derivatives of the modal functions. By including a bandpass filter in the feedback loop, residual vibrations can be attenuated without exciting high-frequency vibrations. The control method is simple to implement; its effectiveness is confirmed by simulation and experimental results.

The effect of microscale random Alfvén waves on the propagation of large-scale Alfvén waves

1983 ◽  
Vol 29 (2) ◽  
pp. 243-253 ◽  
Author(s):  
Tomikazu Namikawa ◽  
Hiromitsu Hamabata
Keyword(s):  
Large Scale ◽  
Ponderomotive Force ◽  
Collisionless Plasma ◽  
Alfven Waves ◽  
Velocity Fields ◽  
Velocity Shear ◽  
Alfvén Waves ◽  
Spectrum Function ◽  
Spatial Derivatives ◽  
Derivatives Of

The ponderomotive force generated by random Alfvén waves in a collisionless plasma is evaluated taking into account mean magnetic and velocity shear and is expressed as a series involving spatial derivatives of mean magnetic and velocity fields whose coefficients are associated with the helicity spectrum function of random velocity field. The effect of microscale random Alfvén waves through ponderomotive and mean electromotive forces generated by them on the propagation of large-scale Alfvén waves is also investigated.

scholarly journals Hexagonal Grid Computation of the Derivatives of the Solution to the Heat Equation by Using Fourth-Order Accurate Two-Stage Implicit Methods

2021 ◽  
Vol 5 (4) ◽  
pp. 203
Author(s):  
Suzan Cival Buranay ◽  
Nouman Arshad ◽  
Ahmed Hersi Matan
Keyword(s):  
Heat Equation ◽  
Fourth Order ◽  
Boundary Value ◽  
Time Variable ◽  
Implicit Methods ◽  
First Order ◽  
Mixed Derivatives ◽  
Hexagonal Grids ◽  
Spatial Derivatives ◽  
Derivatives Of

We give fourth-order accurate implicit methods for the computation of the first-order spatial derivatives and second-order mixed derivatives involving the time derivative of the solution of first type boundary value problem of two dimensional heat equation. The methods are constructed based on two stages: At the first stage of the methods, the solution and its derivative with respect to time variable are approximated by using the implicit scheme in Buranay and Arshad in 2020. Therefore, Oh4+τ of convergence on constructed hexagonal grids is obtained that the step sizes in the space variables x1, x2 and in time variable are indicated by h, 32h and τ, respectively. Special difference boundary value problems on hexagonal grids are constructed at the second stages to approximate the first order spatial derivatives and the second order mixed derivatives of the solution. Further, Oh4+τ order of uniform convergence of these schemes are shown for r=ωτh2≥116,ω>0. Additionally, the methods are applied on two sample problems.

scholarly journals Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
N. Mindu ◽  
D. P. Mason
Keyword(s):  
Conservation Laws ◽  
Power Law ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Multiplier Method ◽  
Reduction Theorem ◽  
Double Reduction ◽  
Exponential Law ◽  
Spatial Derivatives ◽  
Derivatives Of

The derivation of conservation laws for the magma equation using the multiplier method for both the power law and exponential law relating the permeability and matrix viscosity to the voidage is considered. It is found that all known conserved vectors for the magma equation and the new conserved vectors for the exponential laws can be derived using multipliers which depend on the voidage and spatial derivatives of the voidage. It is also found that the conserved vectors are associated with the Lie point symmetry of the magma equation which generates travelling wave solutions which may explain by the double reduction theorem for associated Lie point symmetries why many of the known analytical solutions are travelling waves.

scholarly journals Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 174-187 ◽  
Author(s):  
William Rodi ◽  
Randall L. Mackie
Keyword(s):  
Inverse Problems ◽  
Objective Function ◽  
Complete Solution ◽  
Model Space ◽  
Conjugate Gradients ◽  
Nonlinear Inversion ◽  
Spatial Derivatives ◽  
Computationally Intensive ◽  
Derivatives Of ◽  
Special Case

We investigate a new algorithm for computing regularized solutions of the 2-D magnetotelluric inverse problem. The algorithm employs a nonlinear conjugate gradients (NLCG) scheme to minimize an objective function that penalizes data residuals and second spatial derivatives of resistivity. We compare this algorithm theoretically and numerically to two previous algorithms for constructing such “minimum‐structure” models: the Gauss‐Newton method, which solves a sequence of linearized inverse problems and has been the standard approach to nonlinear inversion in geophysics, and an algorithm due to Mackie and Madden, which solves a sequence of linearized inverse problems incompletely using a (linear) conjugate gradients technique. Numerical experiments involving synthetic and field data indicate that the two algorithms based on conjugate gradients (NLCG and Mackie‐Madden) are more efficient than the Gauss‐Newton algorithm in terms of both computer memory requirements and CPU time needed to find accurate solutions to problems of realistic size. This owes largely to the fact that the conjugate gradients‐based algorithms avoid two computationally intensive tasks that are performed at each step of a Gauss‐Newton iteration: calculation of the full Jacobian matrix of the forward modeling operator, and complete solution of a linear system on the model space. The numerical tests also show that the Mackie‐Madden algorithm reduces the objective function more quickly than our new NLCG algorithm in the early stages of minimization, but NLCG is more effective in the later computations. To help understand these results, we describe the Mackie‐Madden and new NLCG algorithms in detail and couch each as a special case of a more general conjugate gradients scheme for nonlinear inversion.

Peridynamic Modeling of Impact Damage

2004 ◽  
Author(s):  
S. A. Silling ◽  
E. Askari
Keyword(s):  
Impact Damage ◽  
Glass Plate ◽  
Three Dimensional ◽  
Alternative Formulation ◽  
Multiple Impacts ◽  
Peridynamic Theory ◽  
Finite Distance ◽  
Spatial Derivatives ◽  
Damage In Concrete ◽  
Derivatives Of

The peridynamic theory is an alternative formulation of continuum mechanics oriented toward modeling discontinuites such as cracks. It differs from the classical theory and most nonlocal theories in that it does not involve spatial derivatives of the displacement field. Instead, it is formulated in terms of integral equations, whose validity is not affected by the presence of discontinuities such as cracks. It may be thought of as a “continuum version of molecular dynamics” in that particles interact directly with each other across a finite distance. This paper outlines the basis of the peridynamic theory and its numerical implementation in a three-dimensional code called EMU. Examples include simulations of a Charpy V-notch test, accumulated damage in concrete due to multiple impacts, and crack fragmentation of a glass plate.

Thermal stress analysis of in-plane two-directional functionally graded plates subjected to in-plane edge heat fluxes

2016 ◽  
Vol 232 (8) ◽  
pp. 693-716
Author(s):  
MK Apalak ◽  
MD Demirbas
Keyword(s):  
Mechanical Properties ◽  
Thermal Stress ◽  
Functionally Graded ◽  
Heat Fluxes ◽  
Material Composition ◽  
Stress Distributions ◽  
Thermal And Mechanical Properties ◽  
Functionally Graded Plates ◽  
Spatial Derivatives ◽  
Derivatives Of

This study investigates the thermal stress and deformation states of bi-directional functionally graded clamped plates subjected to constant in-plane heat fluxes along two ceramic edges. The material properties of the functionally graded plates were assumed to vary with a power law along two in-plane directions not through the plate thickness direction. The spatial derivatives of thermal and mechanical properties of the material composition were considered, and the effects of the bi-directional composition variations and spatial derivative terms on the displacement, strain and stress distributions were also investigated. The heat conduction and Navier equations describing the two-dimensional thermo-elastic problem were discretized using finite-difference method, and the set of linear equations were solved using the pseudo singular value method. The compositional gradient exponents and the spatial derivatives of thermal and mechanical properties of the material composition were observed to play an important role especially on the heat transfer durations, the displacement and strain distributions, but had a minor effect on the temperature and stress distributions.

scholarly journals Measuring Strain Response Mode Shapes with a Continuous-Scan LDV

2002 ◽  
Vol 9 (1-2) ◽  
pp. 19-27 ◽  
Author(s):  
Anthony B. Stanbridge ◽  
Milena Martarelli ◽  
David J. Ewins
Keyword(s):  
Mode Shape ◽  
Response Mode ◽  
Mode Shapes ◽  
Stress And Strain ◽  
Governing Equations ◽  
Convenient Means ◽  
Straight Line ◽  
Polynomial Series ◽  
Spatial Derivatives ◽  
Derivatives Of

A continuous-scan LDV is a convenient means for measuring the response mode shape (ODS) of a vibrating surface, particularly in view of the fact that the ODS is automatically derived as a spatial polynomial series. Second spatial derivatives of the deflection equations are therefore easily derived, and these should, in principle, give curvature equations from which, for a beam or plate of known cross-section, stresses and strains can be obtained directly. Unfortunately, the stress and strain distributions depend critically on higher terms in the original ODS series, which are not accurately measured. This problem can be avoided by a method described here, which enables accurate stress and strain distributions to be derived, from a straight-line LDV scan along a uniform beam, using only five terms in the mode-shape polynomial series. A similar technique could be applied to uniform plates but the analysis and the governing equations are rather more complicated.

scholarly journals GAUGED LIFSHITZ MODEL WITH CHERN–SIMONS TERM

2013 ◽  
Vol 28 (09) ◽  
pp. 1350025 ◽  
Author(s):  
GUSTAVO S. LOZANO ◽  
FIDEL A. SCHAPOSNIK ◽  
GIANNI TALLARITA
Keyword(s):  
Fourth Order ◽  
Order Term ◽  
Equations Of Motion ◽  
Nontrivial Solutions ◽  
Oscillatory Solutions ◽  
Modulated Phases ◽  
Fourth Order Term ◽  
Spatial Derivatives ◽  
Chern Simons ◽  
Derivatives Of

We present a gauged Lifshitz Lagrangian including second- and fourth-order spatial derivatives of the scalar field and a Chern–Simons term, and study nontrivial solutions of the classical equations of motion. While the coefficient β of the fourth-order term should be positive in order to guarantee positivity of the energy, the coefficient α of the quadratic one need not be. We investigate the parameter domains and find significant differences in the field behaviors. Apart from the usual vortex field behavior of the ordinary relativistic Chern–Simons–Higgs model, we find in certain parameter domains oscillatory solutions reminiscent of the modulated phases of Lifshitz systems.

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