ICACT20220323 Slide.23
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Thank You
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ICACT20220323 Slide.22
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Conclusion
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ICACT20220323 Slide.21
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We will determine beforehand the different values of the functions GaMa(i) = ...
corresponding for each subdomain
GamAi representing a part where there is presence or not of a deposit. These identified values will be stored in a database, as shown in the table below:
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ICACT20220323 Slide.20
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Algorithm to solve the problm in dimension 2
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ICACT20220323 Slide.19
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Modeling equation of the phenomenon in dimension 2
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ICACT20220323 Slide.18
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In dimension 2: Rectangular form
Let O be a bounded and non-empty open set of P known. Let his measure Lebesgue noted my mes(O). GaMa 0 a non-empty part of the adhesion O of the open O.
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ICACT20220323 Slide.17
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Algorithm describing the procedure for determining the values of ai :
1. begin
2. We consider at a breaking point
3. We successively browse the database containing the different pre-recorded nodes to find where is a.
4. If a > ai then g(a) < g(ai)
5. Considering a1 (the first node of known domain), if g(a) > g(a1) then
a1 < a else a > a1 endif
6. We are looking for i0 2 f1; :::ng such that if g(ai0+1) < g(a) < g(ai0)
then ai0+1 < a < ai0 endif
7. endif
8. end
Assuming beforehand that the corresponding u0(ai0) values for each node ai of the domain representing a cable telephone line have been evaluated, measured and recorded in a database, as indicated in the table below:
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ICACT20220323 Slide.16
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for x in R, it is further assumed that c(x) > 0
We also suppose that u'(0) is given, so how can we nd a ( 0 < x < a) for the problem to be posed?
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ICACT20220323 Slide.15
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Domain analysis and identification process in dimension 1:
The phenomenon is modeled by the equation:
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ICACT20220323 Slide.14
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Boundary conditions associated with Helmholtz equation
Existence and unicity of the solution is also proved
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ICACT20220323 Slide.13
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Explanation Continue
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ICACT20220323 Slide.12
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Wave propagation in a transmission medium (coaxial cable in free
space, isotropic medium).
Here the problem is well define and also available in two, three dimension, cylindrical, and spherical.
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ICACT20220323 Slide.11
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Models of problem:
Boundray conditions associated with Laplace equation
Existence and Unicity of the solution
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ICACT20220323 Slide.10
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In this section we describe problem models that justify our theory:
Steam retention in a transmission medium
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ICACT20220323 Slide.09
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Before finding the solution, we make some mathematical reminders on concepts to use in our work. Maximum principle
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ICACT20220323 Slide.08
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Before finding the solution, we make some mathematical reminders on concepts to use in our work.
Distribution theory,
Maximum principle
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ICACT20220323 Slide.07
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In dimension 1:
In dimension 1, the domain to determine the extent is linear. It will suffice to launch the signal at point 0 and to determine its range by identifying the point a.
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ICACT20220323 Slide.06
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Position of the problem: In this section,
If the known edge of a domain is excited by a good signal, then depending on the power we can determine the extent of the global domain
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ICACT20220323 Slide.05
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Position of the problem:
In this section, we show and justify that the problem exists and can be determined as a function of the extent of a space to consider.
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ICACT20220323 Slide.04
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Position of the problem
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ICACT20220323 Slide.03
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The objective of this work, which was conduct was to carry out the determination procedures to identify a domain by looking border (by sending appropriate signals).
We proved that if well-defined signals are sent on the known edge Γ_0 of a regular field Ω of Rn (n=1, 2), where prevail some phenomena modeled by partial derivative equations and that following a certain number of ow measurements on the same edge, knowing ∫_(Γ_0)▒〖∂u/∂n gdΓ〗 (where n indicates the normal external of ∂Ω), it is possible to find a method which leads to the determination of Ω. The demonstration were made in the stationary case with dimension n=1, 2 and arbitrary form.
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ICACT20220323 Slide.02
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The Content of the presentation will focus on:
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ICACT20220323 Slide.01
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Hi everybody, my name is James Tamgno kouawa. To carry out the research work that led to the presentation of this article, the team of the eINOV laboratory of the Ecole Supérieure Multinationale des Télécommunications (ESMT) of Dakar cooperated with the team of researchers from the Laboratoire d'Informatique, de Télécommunications et Applications (LITA) of the Ecole Supérieure Polytechnique (ESP) of Dakar.
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