Is there a reason for why some problems reduce to Caldéron's inverse conductivity equation?
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Is there a reason for why some problems reduce to Caldéron's inverse conductivity equation?
Or is it "coincindence"?
Such problems include, optical tomography, inverse scattering. E.g. in https://ims.nus.edu.sg/events/2018/theo/files/tutn3.pdf
inverse-problems
asked Dec 24 '18 at 18:27
mavaviljmavavilj
2,86211138
$endgroup$
add a comment |
$begingroup$
Is there a reason for why some problems reduce to Caldéron's inverse conductivity equation?
Or is it "coincindence"?
Such problems include, optical tomography, inverse scattering. E.g. in https://ims.nus.edu.sg/events/2018/theo/files/tutn3.pdf
inverse-problems
asked Dec 24 '18 at 18:27
mavaviljmavavilj
2,86211138
$endgroup$
$begingroup$
Can you please provide examples?
$endgroup$
– timur
Dec 24 '18 at 18:34
add a comment |
$begingroup$
Is there a reason for why some problems reduce to Caldéron's inverse conductivity equation?
Or is it "coincindence"?
Such problems include, optical tomography, inverse scattering. E.g. in https://ims.nus.edu.sg/events/2018/theo/files/tutn3.pdf
inverse-problems
asked Dec 24 '18 at 18:27
mavaviljmavavilj
2,86211138
$endgroup$
Is there a reason for why some problems reduce to Caldéron's inverse conductivity equation?
Or is it "coincindence"?
Such problems include, optical tomography, inverse scattering. E.g. in https://ims.nus.edu.sg/events/2018/theo/files/tutn3.pdf
inverse-problems
inverse-problems
asked Dec 24 '18 at 18:27
mavaviljmavavilj
2,86211138
asked Dec 24 '18 at 18:27
mavaviljmavavilj
2,86211138
edited Dec 24 '18 at 18:35
mavavilj
asked Dec 24 '18 at 18:27
mavaviljmavavilj
2,86211138
asked Dec 24 '18 at 18:27
mavaviljmavavilj
2,86211138
asked Dec 24 '18 at 18:27
mavaviljmavavilj
2,86211138
2,86211138
$begingroup$
Can you please provide examples?
$endgroup$
– timur
Dec 24 '18 at 18:34
add a comment |
$begingroup$
Can you please provide examples?
$endgroup$
– timur
Dec 24 '18 at 18:34
$begingroup$
Can you please provide examples?
$endgroup$
– timur
Dec 24 '18 at 18:34
$begingroup$
Can you please provide examples?
$endgroup$
– timur
Dec 24 '18 at 18:34
add a comment |
1 Answer
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Calderón's problem, physically, is a problem of identifying a conductivity parameter in a steady-state (time-independent) diffusion process from particular types of boundary measurements.
If you have a time-dependent physical process that includes diffusion, it might be possible to neglect the non-diffusion terms and to consider a time-independent problem and to consider Dirichlet and Neumann data as relevant. If all of these are possible, you have Calderón's problem.
The above simplifications are justified or flawed based on physical grounds - does the diffusive behaviour dominate the other types of behaviours in the situation? Is the process fast enough to consider the steady state? Do Dirichlet and Neumann boundary conditions have physical meaning and can they be measured and adjusted by the one doing the measurements?
Another connection is the remarkable reduction of Calderón's problem to the (mathematician's) Schrödinger equation. A number of other problems can be reduced to it, or the equation can be a reasonable model of a number of phenomena, based on similar reasoning as above.
answered Dec 31 '18 at 8:37
Tommi BranderTommi Brander
981922
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add a comment |
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1 Answer
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1 Answer
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active
oldest
votes
active
oldest
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active
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$begingroup$
Calderón's problem, physically, is a problem of identifying a conductivity parameter in a steady-state (time-independent) diffusion process from particular types of boundary measurements.
If you have a time-dependent physical process that includes diffusion, it might be possible to neglect the non-diffusion terms and to consider a time-independent problem and to consider Dirichlet and Neumann data as relevant. If all of these are possible, you have Calderón's problem.
The above simplifications are justified or flawed based on physical grounds - does the diffusive behaviour dominate the other types of behaviours in the situation? Is the process fast enough to consider the steady state? Do Dirichlet and Neumann boundary conditions have physical meaning and can they be measured and adjusted by the one doing the measurements?
Another connection is the remarkable reduction of Calderón's problem to the (mathematician's) Schrödinger equation. A number of other problems can be reduced to it, or the equation can be a reasonable model of a number of phenomena, based on similar reasoning as above.
answered Dec 31 '18 at 8:37
Tommi BranderTommi Brander
981922
$endgroup$
add a comment |
$begingroup$
Calderón's problem, physically, is a problem of identifying a conductivity parameter in a steady-state (time-independent) diffusion process from particular types of boundary measurements.
If you have a time-dependent physical process that includes diffusion, it might be possible to neglect the non-diffusion terms and to consider a time-independent problem and to consider Dirichlet and Neumann data as relevant. If all of these are possible, you have Calderón's problem.
The above simplifications are justified or flawed based on physical grounds - does the diffusive behaviour dominate the other types of behaviours in the situation? Is the process fast enough to consider the steady state? Do Dirichlet and Neumann boundary conditions have physical meaning and can they be measured and adjusted by the one doing the measurements?
Another connection is the remarkable reduction of Calderón's problem to the (mathematician's) Schrödinger equation. A number of other problems can be reduced to it, or the equation can be a reasonable model of a number of phenomena, based on similar reasoning as above.
answered Dec 31 '18 at 8:37
Tommi BranderTommi Brander
981922
$endgroup$
add a comment |
$begingroup$
Calderón's problem, physically, is a problem of identifying a conductivity parameter in a steady-state (time-independent) diffusion process from particular types of boundary measurements.
If you have a time-dependent physical process that includes diffusion, it might be possible to neglect the non-diffusion terms and to consider a time-independent problem and to consider Dirichlet and Neumann data as relevant. If all of these are possible, you have Calderón's problem.
The above simplifications are justified or flawed based on physical grounds - does the diffusive behaviour dominate the other types of behaviours in the situation? Is the process fast enough to consider the steady state? Do Dirichlet and Neumann boundary conditions have physical meaning and can they be measured and adjusted by the one doing the measurements?
Another connection is the remarkable reduction of Calderón's problem to the (mathematician's) Schrödinger equation. A number of other problems can be reduced to it, or the equation can be a reasonable model of a number of phenomena, based on similar reasoning as above.
answered Dec 31 '18 at 8:37
Tommi BranderTommi Brander
981922
$endgroup$
Calderón's problem, physically, is a problem of identifying a conductivity parameter in a steady-state (time-independent) diffusion process from particular types of boundary measurements.
If you have a time-dependent physical process that includes diffusion, it might be possible to neglect the non-diffusion terms and to consider a time-independent problem and to consider Dirichlet and Neumann data as relevant. If all of these are possible, you have Calderón's problem.
The above simplifications are justified or flawed based on physical grounds - does the diffusive behaviour dominate the other types of behaviours in the situation? Is the process fast enough to consider the steady state? Do Dirichlet and Neumann boundary conditions have physical meaning and can they be measured and adjusted by the one doing the measurements?
Another connection is the remarkable reduction of Calderón's problem to the (mathematician's) Schrödinger equation. A number of other problems can be reduced to it, or the equation can be a reasonable model of a number of phenomena, based on similar reasoning as above.
answered Dec 31 '18 at 8:37
Tommi BranderTommi Brander
981922
answered Dec 31 '18 at 8:37
Tommi BranderTommi Brander
981922
answered Dec 31 '18 at 8:37
Tommi BranderTommi Brander
981922
answered Dec 31 '18 at 8:37
Tommi BranderTommi Brander
981922
981922
add a comment |
add a comment |
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Can you please provide examples?
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– timur
Dec 24 '18 at 18:34