scholarly journals Geometric shape features extraction using a steady state partial differential equation system

2019 ◽  
Vol 6 (4) ◽  
pp. 647-656 ◽  
Author(s):  
Takayuki Yamada
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Steady State ◽  
Analytical Solution ◽  
Geometric Shape ◽  
Geometrical Shape ◽  
Shape Features ◽  
Partial Differential ◽  
Topological Constraint ◽  
Numerical Examples

Abstract A unified method for extracting geometric shape features from binary image data using a steady-state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to extract the thickness, orientation, and skeleton simultaneously. The main advantage of the proposed method is that the orientation is defined without derivatives and thickness computation is not imposed a topological constraint on the target shape. A one-dimensional analytical solution is provided to validate the proposed method. In addition, two-dimensional numerical examples are presented to confirm the usefulness of the proposed method. Highlights A steady state partial differential equation for extraction of geometrical shape features is formulated. The functions for geometrical shape features are formulated by the solution of the proposed PDE. Analytical solution is provided in one-dimension. Numerical examples are provided in two-dimension.

scholarly journals Sinc-Galerkin method for solving hyperbolic partial differential equations

2018 ◽  
Vol 8 (2) ◽  
pp. 250-258 ◽  
Author(s):  
Aydin Secer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Galerkin Method ◽  
Hyperbolic Equations ◽  
Approximate Solutions ◽  
Equation System ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Numerical Examples

In this work, we consider the hyperbolic equations to determine the approximate solutions via Sinc-Galerkin Method (SGM). Without any numerical integration, the partial differential equation transformed to an algebraic equation system. For the numerical calculations, Maple is used. Several numerical examples are investigated and the results determined from the method are compared with the exact solutions. The results are illustrated both in the table and graphically.

scholarly journals Comparison of Analytical Solution of DGLAP Equations forF2NS(x,t)at Smallxby Two Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Neelakshi N. K. Borah ◽  
D. K. Choudhury ◽  
P. K. Sahariah
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Structure Function ◽  
Method Of Characteristics ◽  
Dglap Equation ◽  
Partial Differential ◽  
Chi Square ◽  
Data Set ◽  
The Method Of Characteristics

The DGLAP equation for the nonsinglet structure functionF2NS(x,t)at LO is solved analytically at lowxby converting it into a partial differential equation in two variables: Bjorkenxandt  (t=ln(Q2/Λ2)and then solved by two methods: Lagrange’s auxiliary method and the method of characteristics. The two solutions are then compared with the available data on the structure function. The relative merits of the two solutions are discussed calculating the chi-square with the used data set.

scholarly journals Nonlinear Models for Transverse Forced Vibration of Axially Moving Viscoelastic Beams

2011 ◽  
Vol 18 (1-2) ◽  
pp. 281-287 ◽  
Author(s):  
Hu Ding ◽  
Li-Qun Chen
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Steady State ◽  
Transverse Vibration ◽  
Nonlinear Models ◽  
Transverse Motion ◽  
Steady State Response ◽  
Partial Differential ◽  
State Response ◽  
Axially Moving

Nonlinear models of transverse vibration of axially moving viscoelastic beams subjected external transverse loads via steady-state periodical response are numerically investigated. An integro-partial-differential equation and a partial-differential equation of transverse motion can be derived respectively from a model of the coupled planar vibration for an axially moving beam. The finite difference scheme is developed to calculate steady-state response for the model of coupled planar and the two models of transverse motion under the simple support boundary. Numerical results indicate that the amplitude of the steady-state response for the model of coupled vibration and two models of transverse vibration predict qualitatively the same tendencies with the changing parameters and the integro-partial-differential equation gives results more closely to the coupled planar vibration.

scholarly journals On closed-form solutions of some nonlinear partial differential equations

2000 ◽  
Vol 23 (2) ◽  
pp. 81-88 ◽  
Author(s):  
S. S. Okoya
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Equation ◽  
Steady State ◽  
Closed Form ◽  
Nonlinear Wave Equation ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Closed Form Solutions ◽  
Thermal Explosion Theory

This paper is devoted to closed-form solutions of the partial differential equation:θxx+θyy+δexp(θ)=0, which arises in the steady state thermal explosion theory. We find simple exact solutions of the formθ(x,y)=Φ(F(x)+G(y)), andθ(x,y)=Φ(f(x+y)+g(x-y)). Also, we study the corresponding nonlinear wave equation.

Inversion-Based and Optimal Feedforward Control for Population Dynamics with Input Constraints and Self-Competition in Chemostat Reactor Applications

2020 ◽  
Author(s):  
Anna-Carina Kurth ◽  
Kevin Schmidt ◽  
Oliver Sawodny
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Steady State ◽  
Feedforward Control ◽  
Reference Trajectory ◽  
Input Constraints ◽  
Partial Differential ◽  
First Order ◽  
Physical Limitations ◽  
Chemostat Reactor

Abstract Through chemostat reactors, organisms can be observed under laboratory conditions. Hereby, the reactor contains the biomass, whose growth can be controlled via the dilution rate respectively the speed of a pump. Due to physical limitations, input constraints need to be considered. The population density in the reactor can be described by a hyperbolic nonlinear integro partial differential equation of first order. The steady-states and generalized eigenvalues and -modes of these integro partial differential equation are determined. In order to track a desired reference trajectory an optimal and an inversion-based feedforward control are designed. For the optimal feedforward control, the singular arc of the control is calculated and a switching strategy is stated, which explicitly considers the input constraints. For the inversion-based feedforward control, the integro partial differential equation is first linearized around the steady-state. To comply with the input constraints a control system simulator is designed. For the simulation model, the integro partial differential equation is approximated using Galerkin's method. Simulations show the functionality of the designed controls and provide the basis for comparison. The inversion-based feedforward control operates well near the steady-state, whereas the performance of the optimal feedforward control is not bounded to the proximity to the steady-state.

Controlling of the Pollution Based on a Prediction Model

2014 ◽  
Vol 513-517 ◽  
pp. 4094-4097
Author(s):  
Jing Mei Yang ◽  
Xiang Hui Zhao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Prediction Model ◽  
Environmental Monitoring ◽  
Partial Differential ◽  
Numerical Examples ◽  
Proposed Model ◽  
Efficient Measures

Controlling of the pollution plays an important role in environmental monitoring. This paper proposed a prediction model for the evolution of pollution in a certain region. With the statistic data of the pollution in this region, several parameters can be determined. With solving the related partial differential equation, the evolution of the pollution in next days can be predicted. Then some efficient measures can be adopted for controlling. The efficiency and the accuracy of the proposed model are shown in presented numerical examples.

Boundary Control of Temperature Distribution in a Rectangular Functionally Graded Material Plate

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Hossein Rastgoftar ◽  
Mohammad Eghtesad ◽  
Alireza Khayatian
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Flux ◽  
Steady State ◽  
Temperature Distribution ◽  
Functionally Graded ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Fg Plates ◽  
Graded Material

In this paper, an analytical method and a partial differential equation based solution to control temperature distribution for functionally graded (FG) plates is introduced. For the rectangular FG plate under consideration, it is assumed that the material properties such as thermal conductivity, density, and specific heat capacity vary in the width direction, and the governing heat conduction equation of the plate is a second-order partial differential equation. Using Lyapunov’s theorem, it is shown that by applying controlled heat flux through the boundary of the domain, the temperature distribution of the plate will approach a desired steady-state distribution. Numerical simulation is provided to verify the effectiveness of the proposed method such that by applying the boundary transient heat flux, in-domain distributed temperature converges to its desired steady-state temperature.

scholarly journals Modified Kudrayshov Method to Solve Generalized Kuramoto–Sivashinsky Equation

2018 ◽  
Author(s):  
Rathinavel Silambarasan ◽  
Adem Kilicman
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Complex Plane ◽  
Exact Analytical Solution ◽  
Nonlinear Partial Differential Equation ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Complex Solutions ◽  
Sivashinsky Equation

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudrayshov equation for the exact analytical solution. The modified Kudrayshov method converts the nonlinear partial differential equation to algebraic equations by results of various steps which on solving the so obtained equation systems yields the analytical solution. By this way various exact including complex solutions are found and drawn their behaviour in complex plane by Maple to compare the uniqueness of various solutions.

Sign in / Sign up

Export Citation Format

Share Document