scholarly journals The enclosure method for inverse obstacle scattering over a finite time interval: VI. Using shell-type initial data

2020 ◽  
Vol 28 (3) ◽  
pp. 349-366
Author(s):  
Masaru Ikehata
Keyword(s):  
Heat Flux ◽  
Coupled System ◽  
The Body ◽  
Time Interval ◽  
Heat Equations ◽  
Finite Time Interval ◽  
Large Parameter ◽  
Inverse Boundary ◽  
Enclosure Method ◽  
Whole Space

AbstractA simple idea of finding a domain that encloses an unknown discontinuity embedded in a body is introduced by considering an inverse boundary value problem for the heat equation. The idea gives a design of a special heat flux on the surface of the body such that from the corresponding temperature field on the surface one can extract the smallest radius of the sphere centered at an arbitrary given point in the whole space and enclosing unknown inclusions. Unlike before, the designed flux is free from a large parameter. An application of the idea to a coupled system of the elastic wave and heat equations are also given.

scholarly journals The enclosure method for the heat equation using time-reversal invariance for a wave equation

2020 ◽  
Vol 28 (1) ◽  
pp. 93-104
Author(s):  
Masaru Ikehata
Keyword(s):  
Heat Flux ◽  
Wave Equation ◽  
Heat Equation ◽  
Time Reversal ◽  
The Body ◽  
Time Interval ◽  
Time Reversal Invariance ◽  
Large Parameter ◽  
Reversal Invariance ◽  
Enclosure Method

AbstractThe heat equation does not have time-reversal invariance. However, using a solution of an associated wave equation which has time-reversal invariance, one can establish an explicit extraction formula of the minimum sphere that is centered at an arbitrary given point and encloses an unknown cavity inside a heat conductive body. The data employed in the formula consist of a special heat flux depending on a large parameter prescribed on the surface of the body over an arbitrary fixed finite time interval and the corresponding temperature field. The heat flux never blows up as the parameter tends to infinity. This is different from a previous formula for the heat equation which also yields the minimum sphere. In this sense, the prescribed heat flux is moderate.

scholarly journals On finding a cavity in a thermoelastic body using a single displacement measurement over a finite time interval on the surface of the body

2018 ◽  
Vol 26 (3) ◽  
pp. 369-394 ◽  
Author(s):  
Masaru Ikehata
Keyword(s):  
Time Domain ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Coupled System ◽  
The Body ◽  
Time Interval ◽  
Heat Equations ◽  
Time Domain Data ◽  
Thermoelastic Body ◽  
The Time Domain

AbstractA mathematical formulation of an estimation problem of a cavity inside a three-dimensional thermoelastic body by using time domain data is considered. The governing equation of the problem is given by a system of equations in the linear theory of thermoelasticity which is a coupled system of the elastic wave and heat equations. A new version of the enclosure method in the time domain which is originally developed for the classical wave equation is established. For a comparison, the results in the decoupled case are also given.

scholarly journals Prescribing a heat flux coming from a wave equation

2019 ◽  
Vol 27 (5) ◽  
pp. 731-744 ◽  
Author(s):  
Masaru Ikehata
Keyword(s):  
Heat Flux ◽  
Asymptotic Behavior ◽  
Wave Equation ◽  
Time Domain ◽  
Indicator Function ◽  
The Body ◽  
Enclosure Method ◽  
Whole Space ◽  
The Time Domain ◽  
Recent Version

Abstract What happens when one prescribes a heat flux which is proportional to the Neumann data of a solution of the wave equation in the whole space on the surface of a heat conductive body? It is shown that there is a difference in the asymptotic behavior of the indicator function in the most recent version of the time domain enclosure method, which aims at extracting information about an unknown cavity embedded in the body.

scholarly journals The enclosure method for inverse obstacle scattering over a finite time interval: V. Using time-reversal invariance

2019 ◽  
Vol 27 (1) ◽  
pp. 133-149 ◽  
Author(s):  
Masaru Ikehata
Keyword(s):  
Wave Equation ◽  
Time Reversal ◽  
Finite Time ◽  
Single Point ◽  
Arbitrary Point ◽  
Time Interval ◽  
Finite Time Interval ◽  
Reversal Invariance ◽  
Enclosure Method ◽  
Space Wave

Abstract The wave equation is time-reversal invariant. The enclosure method, using a Neumann data generated by this invariance, is introduced. The method yields the minimum ball that is centered at a given arbitrary point and encloses an unknown obstacle embedded in a known bounded domain from a single point on the graph of the so-called response operator on the boundary of the domain over a finite time interval. The occurrence of the lacuna in the solution of the free space wave equation is positively used.

scholarly journals The enclosure method for inverse obstacle scattering over a finite time interval: IV. Extraction from a single point on the graph of the response operator

2017 ◽  
Vol 25 (6) ◽  
Author(s):  
Masaru Ikehata
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Finite Time ◽  
Single Point ◽  
Obstacle Problems ◽  
Time Interval ◽  
Finite Time Interval ◽  
Partial Differential ◽  
Response Operator ◽  
Enclosure Method

AbstractA final and maybe the simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a

Preparation and In Vitro Evaluation of Resealed Erythrocytes as A New Trend in Treatment of Asthma

2016 ◽  
Vol 6 (3) ◽  
Author(s):  
Mohammed Ibrahim ◽  
Alaa Zaky ◽  
Mohsen Afouna ◽  
Ahmed Samy
Keyword(s):  
In Vitro Release ◽  
Human Erythrocytes ◽  
The Body ◽  
Blood Levels ◽  
Time Interval ◽  
Burst Release ◽  
Prolonged Release ◽  
Nocturnal Asthma ◽  
Carrier Erythrocytes

Carrier erythrocytes are emerging as one of the most promising biological drug delivery systems investigated in recent decades. Beside its biocompatibility, biodegradability and ability to circulate throughout the body, it has the ability to perform extended release system of the drug for a long period. The ultimate goal of this study is to introduce a new carrier system for Salbutamol, maintaining suitable blood levels for a long time, as atrial to resolve the problems of nocturnal asthma medication Therefore in this work we study the effect of time, temperature as well as concentration on the loading of salbutamol in human erythrocytes to be used as systemic sustained release delivery system for this drug. After the loading process is performed the carrier erythrocytes were physically and cellulary characterized. Also, the in vitro release of salbutamol from carrier erythrocytes was studied over time interval. From the results it was found that, human erythrocytes have been successfully loaded with salbutamol using endocytosis method either at 25 Co or at 37 Co . The highest loaded amount was 3.5 mg/ml and 6.5 mg/ml respectively. Moreover, the percent of cells recovery is 90.7± 1.64%. Hematological parameters and osmotic fragility behavior of salbutamol loaded erythrocytes were similar that of native erythrocytes. Scanning electron microscopy demonstrated that the salbutamol loaded cells has moderate change in the morphology. Salbutamol releasing from carrier cell was 43% after 36 hours in phosphate buffer saline. The releasing pattern of the drug from loaded erythrocytes showed initial burst release in the first hour followed by a very slow release, obeying zero order kinetics. It concluded that salbutamol is successfully entrapped into erythrocytes with acceptable loading parameters and moderate morphological changes, this suggesting that erythrocytes can be used as prolonged release carrier for salbutamol.

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