scholarly journals Stability estimate for the aligned magnetic field in a periodic quantum waveguide from Dirichlet-to-Neumann map

2016 ◽  
Vol 57 (6) ◽  
pp. 061502 ◽  
Author(s):  
Youssef Mejri
Keyword(s):  
Magnetic Field ◽  
Stability Estimate ◽  
Quantum Waveguide ◽  
Dirichlet To Neumann Map ◽  
Aligned Magnetic Field

scholarly journals Inverse Problem: Stability for the aligned magnetic field by the Dirichlet-to-Neumann map for the wave equation in a periodic quantum waveguide

2016 ◽  
Vol Volume 23 - 2016 - Special... ◽  
Author(s):  
Mejri Youssef
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Wave Equation ◽  
Stability Estimate ◽  
Quantum Waveguide ◽  
Magnetic Wave ◽  
Problem Stability ◽  
Problème Inverse ◽  
Dirichlet To Neumann Map ◽  
Aligned Magnetic Field

International audience Dans ce papier, on a prouvé une estimation de stabilité pour le problème inverse de dé-termination du champ magnétique dans l'équation des ondes donné sur un domaine non borné à partir de l'opérateur de Dirichlet-to-Neumann. On a montré un résultat de stabilité pour ce problème inverse, dont la démonstration est basée sur la construction de solutions optique géométrique pour l'équation des ondes avec un potentiel magnétique 1-périodique. ABSTRACT. We consider the boundary inverse problem of determining the aligned magnetic field appearing in the magnetic wave equation in a periodic quantum cylindrical waveguide from boundary observations. The observation is given by the Dirichlet to Neumann map associated to the wave equation. We prove by means of the geometrical optics solutions of the magnetic wave equation that the knowledge of the Dirichlet-to-Neumann map determines uniquely the aligned magnetic field induced by a time independent and 1-periodic magnetic potential. We establish a Hölder-type stability estimate in the inverse problem.

scholarly journals Effect of aligned magnetic field on Casson fluid flow over a stretched surface of non-uniform thickness

2019 ◽  
Vol 8 (1) ◽  
pp. 283-292 ◽  
Author(s):  
R. Saravana ◽  
M. Sailaja ◽  
R. Hemadri Reddy
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Casson Fluid ◽  
Uniform Thickness ◽  
Flow Energy ◽  
Cross Diffusion ◽  
Flow Situation ◽  
Matlab Package ◽  
The Impact ◽  
Aligned Magnetic Field

Abstract In the study, we inspect the impact of cross diffusion and aligned magnetic field on Casson fluid flow along a stretched surface of variable thickness. The differential equations explaining the flow situation have been transitioned with the succor of suited transfigurations. The solution of the problem is achieved by using bvp5c Matlab package. From the solution, it is perceived that the flow, temperature and concentration fields are affected by the sundry physical quantities. Results explored for the flow over a uniform and a non-uniform thickness surfaces. The influence of emerging parameters on the flow, energy and mass transport are discussed with graphical and tabular results. Results show that the thermal, flow and species boundary layers are uneven for the flow over a uniform and non-uniform thickness stretched surfaces.

scholarly journals Numerical study of magnetic particles mixing in waste water under an external magnetic field

2020 ◽  
Vol 69 (3) ◽  
pp. 266-275 ◽  
Author(s):  
Christos Liosis ◽  
Evangelos G. Karvelas ◽  
Theodoros Karakasidis ◽  
Ioannis E. Sarris
Keyword(s):  
Magnetic Field ◽  
Magnetic Particles ◽  
Numerical Study ◽  
Low Frequency ◽  
Water And Wastewater Treatment ◽  
Novel Approach ◽  
Optimal Value ◽  
Frequency Optimum ◽  
Combined Action ◽  
Aligned Magnetic Field

Abstract The combination of nanotechnology and microfluidics may offer an effective water and wastewater treatment. A novel approach combines the use of magnetic particles which can capture heavy metal impurities in microfluidic ducts. The purpose of this study is to investigate the mixing mechanism of two water streams, one with magnetic particles and the other with wastewater. The optimum mixing is obtained when particles are uniformly distributed along the volume of water in the duct for the combined action of a permanent, spatially and temporally aligned magnetic field. Results showed that mixing is enhanced as the frequency of the magnetic field decreases or its amplitude increases, while magnetic gradient is found to play an insignificant role in the present configuration. Moreover, for simulations with low frequency, the mean concentration of particles is found to be twice as high as compared to the cases with higher frequency. Optimum distribution of particles inside the micromixer is observed for the combination of 0.6 T, 8 T/m and 5 Hz for the magnetic magnitude, gradient and frequency, respectively, where concentration reaches the optimal value of 0.77 mg/mL along the volume of the duct.

Stability estimate for an inverse problem of the convection-diffusion equation

2020 ◽  
Vol 28 (1) ◽  
pp. 71-92
Author(s):  
Mourad Bellassoued ◽  
Imen Rassas
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Scalar Potential ◽  
Stability Estimate ◽  
Inverse Boundary ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
First Order ◽  
Order Coefficient ◽  
Dirichlet To Neumann Map

AbstractWe consider the inverse boundary value problem for the dynamical steady-state convection-diffusion equation. We prove that the first-order coefficient and the scalar potential are uniquely determined by the Dirichlet-to-Neumann map. More precisely, we show in dimension {n\geq 3} a log-type stability estimate for the inverse problem under consideration. The method is based on reducing our problem to an auxiliary inverse problem and the construction of complex geometrical optics solutions of this problem.

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