Nonlinear partial differential equation modeling and adaptive fault‐tolerant vibration control of flexible rotatable manipulator in three‐dimensional space

2021 ◽  
Author(s):  
Jiacheng Wang ◽  
Fangfei Cao ◽  
Jinkun Liu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Vibration Control ◽  
Fault Tolerant ◽  
Dimensional Space ◽  
Nonlinear Partial Differential Equation ◽  
Three Dimensional ◽  
Equation Modeling ◽  
Differential Equation Modeling ◽  
Three Dimensional Space

Straightforward derivation of Hubral’s wavefront curvature differential equation in inhomogeneous isotropic media

Geophysics ◽  
1980 ◽  
Vol 45 (5) ◽  
pp. 964-967 ◽  
Author(s):  
Theodor Krey
Keyword(s):  
Differential Equation ◽  
Arbitrary Function ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Inhomogeneous Media ◽  
Isotropic Media ◽  
Three Dimensional Space

“Wavefront curvatures in three‐dimensional laterally inhomogeneous media with curved interfaces” (Hubral, 1980, this issue) shows a differential equation [formula (4.1)] which describes the alteration of the wavefront curvature matrix along a raypath in the case of an isotropic velocity v which is an arbitrary function of the locus in the three‐dimensional space. Hubral derives his equation by referring to papers of Popov and Pšenčik (1976, 1978) and Hubral (1979).

XVIII.—The Equation of Conduction of Heat

1926 ◽  
Vol 45 (3) ◽  
pp. 230-244 ◽  
Author(s):  
Marion C. Gray
Keyword(s):  
Differential Equation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Infinite Cylinder ◽  
Image Position ◽  
Three Dimensional Space

The differential equation of the conduction of heat in ordinary three-dimensional space is generally written in the formwhere v denotes the temperature of the medium at time t. For a medium in which the temperature varies only in one direction, e.g. an infinite cylinder with the temperature varying along the axis, the equation is

NUMERICAL SIMULATIONS OF A NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATION MODELING PHYTOPLANKTON AGGREGATION

2015 ◽  
Vol 23 (04) ◽  
pp. 1550032 ◽  
Author(s):  
NADJIA EL SAADI ◽  
ALASSANE BAH
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stochastic Partial Differential Equation ◽  
Stochastic Equation ◽  
Numerical Solutions ◽  
Equation Modeling ◽  
Partial Differential ◽  
Nonlinear Reaction ◽  
Differential Equation Modeling ◽  
Parameter Values

In this paper, we are interested in the numerical simulation of a nonlinear stochastic partial differential equation (SPDE) arising as a model of phytoplankton aggregation. This SPDE consists of a diffusion equation with a chemotaxis term and a branching noise. We develop and implement a numerical scheme to solve this SPDE and present its numerical solutions for parameter values corresponding to real conditions in nature. Further, a comparison is made with two deterministic versions of the SPDE, that are advection–diffusion equations with linear and nonlinear reaction terms, to emphasize the efficiency of the stochastic equation in modeling the aggregation behavior in phytoplankton.

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