hi all,
There is attached a document where we see that the particle noise power is inversely proportional to the receiver radius.
In the previous mail, Max you commented that meausured fluctuations can be cut down taking as a measure the average value within a time interval smaller than the correlation time, and you said this correlation time is equal to the radius of the receiver squared and divided by the diffusion coefficient, could you explain something else about how you find this value?
Regards
Dear Nora, In the past days I was working tight on my paper and I did not have the chance to write a full reply to your email. I'll try to answer to your questions and add some comments in the following.
Yes, the fluctuations you see are due to the what I call particle counting noise, meaning that at the receiver, in order to read the concentration, you're counting the particles inside the spherical boundary for each time instant. If this number is fluctuating, then you can see fluctuations in the concentration measure. The particles fluctuate indeed even if the concentration is kept constant due to the Brownian motion, which makes some of the particles leave the receptor space or enter the receptor space. Therefore, for each time instant the number of particles inside the receptor space is not constant, even if on average (for a concentration kept constant for infinite time...) the read concentration should be equal to the actual concentration of particles in the space.
The inverse proportionality of the power of the noise with respect to the radius of the receiver is indeed right and it matches with the considerations I did for the particle counting noise. Here you'll find attached a brief explanation I wrote for the particle counting noise, including the definition of the correlation time and its application to the noise power formula.
Please, let me know if you have any comment/suggestion or question on the things I wrote.
See you all soon, Max
-----Original Message----- From: n3-tech-bounces@n3cat.upc.edu [mailto:n3-tech-bounces@n3cat.upc.edu] On Behalf Of garralda@ac.upc.edu Sent: Monday, May 03, 2010 11:53 AM To: n3-tech@n3cat.upc.edu Subject: [N3-tech] Counting particle noise
hi all,
There is attached a document where we see that the particle noise power is inversely proportional to the receiver radius.
In the previous mail, Max you commented that meausured fluctuations can be cut down taking as a measure the average value within a time interval smaller than the correlation time, and you said this correlation time is equal to the radius of the receiver squared and divided by the diffusion coefficient, could you explain something else about how you find this value?
Regards
Hi all,
Thanks Max and Luisca for your insightful comments. Are you available next Monday at 10 AM for a videoconference? We would discuss Max's noise findings and the latest simulation results obtained by Nora. Yours,
Nacho
Al 06/05/2010 22:27, En/na Massimiliano Pierobon ha escrit:
Dear Nora, In the past days I was working tight on my paper and I did not have the chance to write a full reply to your email. I'll try to answer to your questions and add some comments in the following.
Yes, the fluctuations you see are due to the what I call particle counting noise, meaning that at the receiver, in order to read the concentration, you're counting the particles inside the spherical boundary for each time instant. If this number is fluctuating, then you can see fluctuations in the concentration measure. The particles fluctuate indeed even if the concentration is kept constant due to the Brownian motion, which makes some of the particles leave the receptor space or enter the receptor space. Therefore, for each time instant the number of particles inside the receptor space is not constant, even if on average (for a concentration kept constant for infinite time...) the read concentration should be equal to the actual concentration of particles in the space.
The inverse proportionality of the power of the noise with respect to the radius of the receiver is indeed right and it matches with the considerations I did for the particle counting noise. Here you'll find attached a brief explanation I wrote for the particle counting noise, including the definition of the correlation time and its application to the noise power formula.
Please, let me know if you have any comment/suggestion or question on the things I wrote.
See you all soon, Max
-----Original Message----- From: n3-tech-bounces@n3cat.upc.edu [mailto:n3-tech-bounces@n3cat.upc.edu] On Behalf Of garralda@ac.upc.edu Sent: Monday, May 03, 2010 11:53 AM To: n3-tech@n3cat.upc.edu Subject: [N3-tech] Counting particle noise
hi all,
There is attached a document where we see that the particle noise power is inversely proportional to the receiver radius.
In the previous mail, Max you commented that meausured fluctuations can be cut down taking as a measure the average value within a time interval smaller than the correlation time, and you said this correlation time is equal to the radius of the receiver squared and divided by the diffusion coefficient, could you explain something else about how you find this value?
Regards
n3-tech mailing list n3-tech@n3cat.upc.edu http://mail.n3cat.upc.edu/cgi-bin/mailman/listinfo/n3-tech
Hi All,
Me and Luisca will be available next Monday at 10am for a skype call.
Talk to you on Monday,
Max
From: n3-tech-bounces@n3cat.upc.edu [mailto:n3-tech-bounces@n3cat.upc.edu] On Behalf Of Ignacio Llatser Martí Sent: Friday, May 07, 2010 6:05 AM To: n3-tech@n3cat.upc.edu Subject: Re: [N3-tech] Counting particle noise
Hi all,
Thanks Max and Luisca for your insightful comments. Are you available next Monday at 10 AM for a videoconference? We would discuss Max's noise findings and the latest simulation results obtained by Nora. Yours,
Nacho
Al 06/05/2010 22:27, En/na Massimiliano Pierobon ha escrit:
Dear Nora, In the past days I was working tight on my paper and I did not have the chance to write a full reply to your email. I'll try to answer to your questions and add some comments in the following.
Yes, the fluctuations you see are due to the what I call particle counting noise, meaning that at the receiver, in order to read the concentration, you're counting the particles inside the spherical boundary for each time instant. If this number is fluctuating, then you can see fluctuations in the concentration measure. The particles fluctuate indeed even if the concentration is kept constant due to the Brownian motion, which makes some of the particles leave the receptor space or enter the receptor space. Therefore, for each time instant the number of particles inside the receptor space is not constant, even if on average (for a concentration kept constant for infinite time...) the read concentration should be equal to the actual concentration of particles in the space.
The inverse proportionality of the power of the noise with respect to the radius of the receiver is indeed right and it matches with the considerations I did for the particle counting noise. Here you'll find attached a brief explanation I wrote for the particle counting noise, including the definition of the correlation time and its application to the noise power formula.
Please, let me know if you have any comment/suggestion or question on the things I wrote.
See you all soon, Max
-----Original Message----- From: n3-tech-bounces@n3cat.upc.edu [mailto:n3-tech-bounces@n3cat.upc.edu] On Behalf Of garralda@ac.upc.edu Sent: Monday, May 03, 2010 11:53 AM To: n3-tech@n3cat.upc.edu Subject: [N3-tech] Counting particle noise
hi all,
There is attached a document where we see that the particle noise power is inversely proportional to the receiver radius.
In the previous mail, Max you commented that meausured fluctuations can be cut down taking as a measure the average value within a time interval smaller than the correlation time, and you said this correlation time is equal to the radius of the receiver squared and divided by the diffusion coefficient, could you explain something else about how you find this value?
Regards
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garralda＠ac.upc.edu -
Ignacio Llatser Martí -
Massimiliano Pierobon