Pretreatment on Initial Value of Image Restoration Models with Different Boundary Conditions

2011 ◽  
Author(s):  
Yuying Shi ◽  
Wen Jia ◽  
Jing Xu
Keyword(s):  
Boundary Conditions ◽  
Image Restoration ◽  
Initial Value ◽  
Different Boundary Conditions

scholarly journals Analysis of Different Boundary Conditions on Homogeneous One-Dimensional Heat Equation

2021 ◽  
Vol 7 (1) ◽  
pp. 15-21
Author(s):  
Norazlina Subani ◽  
Muhammad Aniq Qayyum Mohamad Sukry ◽  
Muhammad Arif Hannan ◽  
Faizzuddin Jamaluddin ◽  
Ahmad Danial Hidayatullah Badrolhisam
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Initial Value ◽  
Partial Differential ◽  
Different Boundary Conditions ◽  
One Dimensional ◽  
Profile Changes ◽  
The Right

Partial differential equations involve results of unknown functions when there are multiple independent variables. There is a need for analytical solutions to ensure partial differential equations could be solved accurately. Thus, these partial differential equations could be solved using the right initial and boundaries conditions. In this light, boundary conditions depend on the general solution; the partial differential equations should present particular solutions when paired with varied boundary conditions. This study analysed the use of variable separation to provide an analytical solution of the homogeneous, one-dimensional heat equation. This study is applied to varied boundary conditions to examine the flow attributes of the heat equation. The solution is verified through different boundary conditions: Dirichlet, Neumann, and mixed-insulated boundary conditions. the initial value was kept constant despite the varied boundary conditions. There are two significant findings in this study. First, the temperature profile changes are influenced by the boundary conditions, and that the boundary conditions are dependent on the heat equation’s flow attributes.

scholarly journals Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

2021 ◽  
Author(s):  
Jacopo Quaglierini ◽  
Alessandro Lucantonio ◽  
Antonio DeSimone
Keyword(s):  
Boundary Conditions ◽  
Elastic Properties ◽  
Central Region ◽  
Mechanical Response ◽  
Different Boundary Conditions ◽  
Kirchhoff Rods ◽  
Model Versus ◽  
The Individual ◽  
Opposite Chirality

Abstract Nature and technology often adopt structures that can be described as tubular helical assemblies. However, the role and mechanisms of these structures remain elusive. In this paper, we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchhoff rods, arranged in pairs with opposite chirality and connected by pin joints, both analytically and numerically. We first focus on compression and find that, whereas a single helical rod would buckle, the rods of the assembly deform coherently as stable helical shapes wound around a common axis. Moreover, we investigate the response of the assembly under different boundary conditions, highlighting the emergence of a central region where rods remain circular helices. Secondly, we study the effects of different hypotheses on the elastic properties of rods, i.e., stress-free rods when straight versus when circular helices, Kirchhoff’s rod model versus Sadowsky’s ribbon model. Summing up, our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods, as well as some interesting features, and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology. Graphic Abstract We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

Thermal phase transition behaviours of the blue phase of bent-core nematogen and chiral dopant mixtures under different boundary conditions

Soft Matter ◽  
2014 ◽  
Vol 10 (41) ◽  
pp. 8224-8228 ◽  
Author(s):  
Min-Jun Gim ◽  
Gohyun Han ◽  
Suk-Won Choi ◽  
Dong Ki Yoon
Keyword(s):  
Phase Transition ◽  
Boundary Conditions ◽  
Liquid Crystalline ◽  
Isotropic Phase ◽  
Different Boundary Conditions ◽  
Various Boundary Conditions ◽  
Thermal Phase Transition ◽  
Thermal Phase ◽  
Blue Phase ◽  
Chiral Dopants

We have investigated dramatic changes in the thermal phase transition of a liquid-crystalline (LC) blue phase (BP) consisting of bent-core nematogen and chiral dopants under various boundary conditions during cooling from the isotropic phase.

Experimental Validation and Numerical Simulation of Shape Memory Flat Wire Actuators

2014 ◽  
Author(s):  
Alexander Czechowicz ◽  
Sven Langbein
Keyword(s):  
Shape Memory Alloy ◽  
Boundary Conditions ◽  
Shape Memory ◽  
Smart Materials ◽  
Empirical Data ◽  
Dynamic Properties ◽  
Fatigue Behavior ◽  
Different Boundary Conditions ◽  
Heating And Cooling ◽  
Actual Shape

Shape memory alloys (SMA) are thermally activated smart materials. Due to their ability to change into a previously imprinted actual shape through the means of thermal activation, they are suitable as actuators for mechatronical systems. Despite of the advantages shape memory alloy actuators provide, these elements are only seldom integrated by engineers into mechatronical systems. Reasons are the complex characteristics, especially at different boundary conditions and the missing simulation- and design tools. Also the lack of knowledge and empirical data are a reason why development projects with shape memory actuators often lead to failures. This paper deals with the dynamic properties of SMA-actuators (Shape Memory Alloy) — characterized by their rate of heating and cooling procedures — that today can only be described insufficiently for different boundary conditions. Based on an analysis of energy fluxes into and out of the actuator, a numerical model of flat-wire used in a bow-like structure, implemented in MATLAB/SIMULINK, is presented. Different actuation parameters, depending on the actuator-geometry and temperature are considered in the simulation in real time. Additionally this publication sums up the needed empirical data (e.g. fatigue behavior) in order to validate the numerical two dimensional model and presents empirical data on SMA flat wire material.

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