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| hi everybody I'm rumen and today I will |
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| hi everybody I'm rumen and today I will |
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| hi everybody I'm rumen and today I will |
| talk about three things optical trapping |
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| talk about three things optical trapping |
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| align:start position:0% |
| talk about three things optical trapping |
| the Boltzmann constant and Brownian |
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| the Boltzmann constant and Brownian |
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| the Boltzmann constant and Brownian |
| motion the goal of the lab is to extract |
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| motion the goal of the lab is to extract |
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| motion the goal of the lab is to extract |
| Boltzmann's constant out of Brownian |
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| Boltzmann's constant out of Brownian |
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| Boltzmann's constant out of Brownian |
| motion and there are two key components |
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| motion and there are two key components |
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| motion and there are two key components |
| to think about first one is the |
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| to think about first one is the |
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| to think about first one is the |
| Boltzmann constant which is prevalent in |
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| Boltzmann constant which is prevalent in |
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| Boltzmann constant which is prevalent in |
| different types of science for example |
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| different types of science for example |
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| different types of science for example |
| we can have it in biophysics where |
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| we can have it in biophysics where |
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| we can have it in biophysics where |
| people use the Boltzmann constant to try |
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| people use the Boltzmann constant to try |
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| people use the Boltzmann constant to try |
| to understand forces in a cellular level |
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| to understand forces in a cellular level |
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| to understand forces in a cellular level |
| we have it in thermodynamics with the |
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| we have it in thermodynamics with the |
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| we have it in thermodynamics with the |
| famous equipartition theorem how does |
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| famous equipartition theorem how does |
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| famous equipartition theorem how does |
| this relate to the Brownian motion the |
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| this relate to the Brownian motion the |
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| this relate to the Brownian motion the |
| key thing is to think about length |
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| key thing is to think about length |
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| key thing is to think about length |
| scales Brownian motion is relevant in |
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| scales Brownian motion is relevant in |
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| scales Brownian motion is relevant in |
| terms of microns and at the same time if |
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| terms of microns and at the same time if |
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| terms of microns and at the same time if |
| we look at the cellular level for |
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| we look at the cellular level for |
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| we look at the cellular level for |
| example if we look at our hair we have |
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| example if we look at our hair we have |
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| example if we look at our hair we have |
| micron sized hair all right so there are |
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| micron sized hair all right so there are |
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| micron sized hair all right so there are |
| different ways to measure the |
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| different ways to measure the |
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| different ways to measure the |
| Boltzmann's constant some people measure |
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| Boltzmann's constant some people measure |
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| Boltzmann's constant some people measure |
| the speed of sound in argon gas others |
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| the speed of sound in argon gas others |
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| the speed of sound in argon gas others |
| do optical trapping in air we will do |
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| do optical trapping in air we will do |
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| do optical trapping in air we will do |
| slightly different optical trapping as |
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| slightly different optical trapping as |
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| slightly different optical trapping as |
| you will see but the consensus among the |
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| you will see but the consensus among the |
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| you will see but the consensus among the |
| scientific community is that it is |
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| scientific community is that it is |
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| scientific community is that it is |
| challenging our plan is to prepare |
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| challenging our plan is to prepare |
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| challenging our plan is to prepare |
| Brownian particles and control their |
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| Brownian particles and control their |
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| Brownian particles and control their |
| Brownian motion we take glass beads of |
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| Brownian motion we take glass beads of |
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| Brownian motion we take glass beads of |
| their spherical glass beads of diameter |
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| their spherical glass beads of diameter |
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| their spherical glass beads of diameter |
| of 3.2 microns and the main to is to |
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| of 3.2 microns and the main to is to |
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| of 3.2 microns and the main to is to |
| concentrate a highly focused lasers on |
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| concentrate a highly focused lasers on |
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| concentrate a highly focused lasers on |
| top of these beads there's interesting |
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| top of these beads there's interesting |
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| top of these beads there's interesting |
| physics going on light carries momentum |
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| physics going on light carries momentum |
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| physics going on light carries momentum |
| versa generates force we have that the |
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| versa generates force we have that the |
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| versa generates force we have that the |
| net gradient force opposes the motion of |
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| net gradient force opposes the motion of |
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| net gradient force opposes the motion of |
| the beam while the net scattering force |
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| the beam while the net scattering force |
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| the beam while the net scattering force |
| goes along the motion of the beam and |
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| goes along the motion of the beam and |
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| goes along the motion of the beam and |
| when these two forces balance each other |
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| when these two forces balance each other |
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| when these two forces balance each other |
| we have a beat that is at the center |
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| we have a beat that is at the center |
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| we have a beat that is at the center |
| when you push this beat a little bit to |
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| when you push this beat a little bit to |
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| when you push this beat a little bit to |
| the left or to the right then we have |
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| the left or to the right then we have |
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| the left or to the right then we have |
| that the gradient forces are pulling |
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| that the gradient forces are pulling |
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| that the gradient forces are pulling |
| back in the center and essentially we |
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| back in the center and essentially we |
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| back in the center and essentially we |
| observe a simple harmonic motion in a |
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| observe a simple harmonic motion in a |
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| observe a simple harmonic motion in a |
| more concrete example what we did is we |
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| more concrete example what we did is we |
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| more concrete example what we did is we |
| took samples and we can find everything |
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| took samples and we can find everything |
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| took samples and we can find everything |
| into a two-dimensional plane this is |
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| into a two-dimensional plane this is |
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| into a two-dimensional plane this is |
| very important we have two directions |
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| very important we have two directions |
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| very important we have two directions |
| the X direction in the Y direction for |
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| the X direction in the Y direction for |
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| the X direction in the Y direction for |
| the beads we put them into water and |
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| the beads we put them into water and |
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| the beads we put them into water and |
| source of Brownian motion comes from the |
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| source of Brownian motion comes from the |
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| source of Brownian motion comes from the |
| collisions between our bead with the |
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| collisions between our bead with the |
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| collisions between our bead with the |
| molecules into the water |
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| molecules into the water |
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| molecules into the water |
| these are thermal collisions that |
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| these are thermal collisions that |
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| these are thermal collisions that |
| generate Brownian motion as you can see |
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| generate Brownian motion as you can see |
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| generate Brownian motion as you can see |
| this lonely beat has its Brownian motion |
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| this lonely beat has its Brownian motion |
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| this lonely beat has its Brownian motion |
| what's interesting is when we shine |
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| what's interesting is when we shine |
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| what's interesting is when we shine |
| light on top of a beat we trap this beat |
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| light on top of a beat we trap this beat |
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| light on top of a beat we trap this beat |
| and we can find the Brownian motion so |
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| and we can find the Brownian motion so |
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| and we can find the Brownian motion so |
| it's feasible to measure the motion and |
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| it's feasible to measure the motion and |
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| it's feasible to measure the motion and |
| the theory behind this is very beautiful |
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| the theory behind this is very beautiful |
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| the theory behind this is very beautiful |
| it's about the equipartition theorem |
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| it's about the equipartition theorem |
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| it's about the equipartition theorem |
| which relates the kinetic energy coming |
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| which relates the kinetic energy coming |
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| which relates the kinetic energy coming |
| from the simple harmonic motion on the |
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| from the simple harmonic motion on the |
| |
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| from the simple harmonic motion on the |
| left-hand side with the thermal energy |
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| left-hand side with the thermal energy |
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| left-hand side with the thermal energy |
| of due to the degrees of freedom now let |
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| of due to the degrees of freedom now let |
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| of due to the degrees of freedom now let |
| us recall that we have a two-dimensional |
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| us recall that we have a two-dimensional |
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| us recall that we have a two-dimensional |
| confinement so we have a direction in X |
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| confinement so we have a direction in X |
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| confinement so we have a direction in X |
| and direction in Y so it means that in |
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| and direction in Y so it means that in |
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| and direction in Y so it means that in |
| each of the directions we have one |
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| each of the directions we have one |
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| each of the directions we have one |
| degree of freedom which is correlated |
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| degree of freedom which is correlated |
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| degree of freedom which is correlated |
| with this equipartition theorem now an |
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| with this equipartition theorem now an |
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| with this equipartition theorem now an |
| interesting thing about the statistical |
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| interesting thing about the statistical |
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| interesting thing about the statistical |
| motion of the molecules is that we have |
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| motion of the molecules is that we have |
| |
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| motion of the molecules is that we have |
| the simple harmonic motion however the |
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| the simple harmonic motion however the |
| |
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| the simple harmonic motion however the |
| things are moving into water so there is |
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| things are moving into water so there is |
| |
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| things are moving into water so there is |
| a drag force that dominates so we |
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| a drag force that dominates so we |
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| a drag force that dominates so we |
| simplify the left hand side what is very |
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| simplify the left hand side what is very |
| |
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| simplify the left hand side what is very |
| interesting is the F factor which comes |
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| interesting is the F factor which comes |
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| align:start position:0% |
| interesting is the F factor which comes |
| from the collisions between the beat |
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| from the collisions between the beat |
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| from the collisions between the beat |
| with the molecules this generates |
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| with the molecules this generates |
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| with the molecules this generates |
| forcing and driving of the simple |
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| forcing and driving of the simple |
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| forcing and driving of the simple |
| harmonic motion I like to point out one |
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| harmonic motion I like to point out one |
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| harmonic motion I like to point out one |
| thing about the scales of the forces we |
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| thing about the scales of the forces we |
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| thing about the scales of the forces we |
| have Pico Newton's which is relevant for |
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| have Pico Newton's which is relevant for |
| |
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| have Pico Newton's which is relevant for |
| optical trapping and for Brownian motion |
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| optical trapping and for Brownian motion |
| |
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| optical trapping and for Brownian motion |
| this is the first observation that we |
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| this is the first observation that we |
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| this is the first observation that we |
| did and actually Einstein this operation |
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| did and actually Einstein this operation |
| |
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| did and actually Einstein this operation |
| a long time ago he observed the white |
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| a long time ago he observed the white |
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| a long time ago he observed the white |
| noise essentially the collisions they |
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| noise essentially the collisions they |
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| noise essentially the collisions they |
| generate uncorrelated forcing and we can |
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| generate uncorrelated forcing and we can |
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| generate uncorrelated forcing and we can |
| think of it as something that is not |
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| think of it as something that is not |
| |
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| think of it as something that is not |
| biased with any distribution is just |
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| biased with any distribution is just |
| |
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| biased with any distribution is just |
| uniform as you can see on these slides |
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| uniform as you can see on these slides |
| |
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| uniform as you can see on these slides |
| we have the position plotted in terms of |
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| we have the position plotted in terms of |
| |
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| we have the position plotted in terms of |
| and it exhibits a uniform distribution |
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| and it exhibits a uniform distribution |
| |
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| and it exhibits a uniform distribution |
| of the spectrum another thing that I |
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| of the spectrum another thing that I |
| |
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| align:start position:0% |
| of the spectrum another thing that I |
| would like to point out is to look at |
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| would like to point out is to look at |
| |
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| align:start position:0% |
| would like to point out is to look at |
| this plot of fluctuations in X&Y and the |
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| this plot of fluctuations in X&Y and the |
| |
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| align:start position:0% |
| this plot of fluctuations in X&Y and the |
| power which is linear with the current |
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| power which is linear with the current |
| |
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| align:start position:0% |
| power which is linear with the current |
| of the lasers as you can see as the |
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| of the lasers as you can see as the |
| |
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| of the lasers as you can see as the |
| power becomes big this means that we are |
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| power becomes big this means that we are |
| |
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| align:start position:0% |
| power becomes big this means that we are |
| trapping more so we have less |
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| trapping more so we have less |
| |
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| align:start position:0% |
| trapping more so we have less |
| fluctuations which is something as |
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| fluctuations which is something as |
| |
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| align:start position:0% |
| fluctuations which is something as |
| expected all right so let's figure out |
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| align:start position:0% |
| expected all right so let's figure out |
| |
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| align:start position:0% |
| expected all right so let's figure out |
| what we want to do with this lab we have |
|
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| align:start position:0% |
| what we want to do with this lab we have |
| |
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| align:start position:0% |
| what we want to do with this lab we have |
| the equipartition theorem and |
|
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| align:start position:0% |
| the equipartition theorem and |
| |
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| align:start position:0% |
| the equipartition theorem and |
| essentially we have three components |
|
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| align:start position:0% |
| essentially we have three components |
| |
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| align:start position:0% |
| essentially we have three components |
| that we would like to measure in order |
|
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| align:start position:0% |
| that we would like to measure in order |
| |
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| align:start position:0% |
| that we would like to measure in order |
| to extract Kb we need to find the |
|
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| align:start position:0% |
| to extract Kb we need to find the |
| |
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| align:start position:0% |
| to extract Kb we need to find the |
| fluctuations which I just presented to |
|
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| align:start position:0% |
| fluctuations which I just presented to |
| |
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| align:start position:0% |
| fluctuations which I just presented to |
| you we need to find the stiffness |
|
|
| align:start position:0% |
| you we need to find the stiffness |
| |
|
|
| align:start position:0% |
| you we need to find the stiffness |
| coefficient alpha which is related to |
|
|
| align:start position:0% |
| coefficient alpha which is related to |
| |
|
|
| align:start position:0% |
| coefficient alpha which is related to |
| the spring constant of motion and then |
|
|
| align:start position:0% |
| the spring constant of motion and then |
| |
|
|
| align:start position:0% |
| the spring constant of motion and then |
| we need to measure the temperature T the |
|
|
| align:start position:0% |
| we need to measure the temperature T the |
| |
|
|
| align:start position:0% |
| we need to measure the temperature T the |
| apparatus that we use has two main |
|
|
| align:start position:0% |
| apparatus that we use has two main |
| |
|
|
| align:start position:0% |
| apparatus that we use has two main |
| components the two components are |
|
|
| align:start position:0% |
| components the two components are |
| |
|
|
| align:start position:0% |
| components the two components are |
| concerned with the two types of light |
|
|
| align:start position:0% |
| concerned with the two types of light |
| |
|
|
| align:start position:0% |
| concerned with the two types of light |
| that we use in our experiment we use a |
|
|
| align:start position:0% |
| that we use in our experiment we use a |
| |
|
|
| align:start position:0% |
| that we use in our experiment we use a |
| laser that shines on top of the confined |
|
|
| align:start position:0% |
| laser that shines on top of the confined |
| |
|
|
| align:start position:0% |
| laser that shines on top of the confined |
| two-dimensional samples and tries to |
|
|
| align:start position:0% |
| two-dimensional samples and tries to |
| |
|
|
| align:start position:0% |
| two-dimensional samples and tries to |
| trap a beat the scatter light from the |
|
|
| align:start position:0% |
| trap a beat the scatter light from the |
| |
|
|
| align:start position:0% |
| trap a beat the scatter light from the |
| laser goes into a QP D a quadrant photo |
|
|
| align:start position:0% |
| laser goes into a QP D a quadrant photo |
| |
|
|
| align:start position:0% |
| laser goes into a QP D a quadrant photo |
| detector which is an ultra-fast camera |
|
|
| align:start position:0% |
| detector which is an ultra-fast camera |
| |
|
|
| align:start position:0% |
| detector which is an ultra-fast camera |
| that manages to quickly digitalize the |
|
|
| align:start position:0% |
| that manages to quickly digitalize the |
| |
|
|
| align:start position:0% |
| that manages to quickly digitalize the |
| content and give us the position of the |
|
|
| align:start position:0% |
| content and give us the position of the |
| |
|
|
| align:start position:0% |
| content and give us the position of the |
| scattered light so when we trap the beat |
|
|
| align:start position:0% |
| scattered light so when we trap the beat |
| |
|
|
| align:start position:0% |
| scattered light so when we trap the beat |
| we know where it is by observing the |
|
|
| align:start position:0% |
| we know where it is by observing the |
| |
|
|
| align:start position:0% |
| we know where it is by observing the |
| feedback from the QPD the other |
|
|
| align:start position:0% |
| feedback from the QPD the other |
| |
|
|
| align:start position:0% |
| feedback from the QPD the other |
| interesting part of the apparatus is the |
|
|
| align:start position:0% |
| interesting part of the apparatus is the |
| |
|
|
| align:start position:0% |
| interesting part of the apparatus is the |
| LED light which illuminates the sample |
|
|
| align:start position:0% |
| LED light which illuminates the sample |
| |
|
|
| align:start position:0% |
| LED light which illuminates the sample |
| and then it brings it to the CCD camera |
|
|
| align:start position:0% |
| and then it brings it to the CCD camera |
| |
|
|
| align:start position:0% |
| and then it brings it to the CCD camera |
| and this is very important so the CCD |
|
|
| align:start position:0% |
| and this is very important so the CCD |
| |
|
|
| align:start position:0% |
| and this is very important so the CCD |
| camera is very slow it cannot measure |
|
|
| align:start position:0% |
| camera is very slow it cannot measure |
| |
|
|
| align:start position:0% |
| camera is very slow it cannot measure |
| Brownian motion what it can do is it can |
|
|
| align:start position:0% |
| Brownian motion what it can do is it can |
| |
|
|
| align:start position:0% |
| Brownian motion what it can do is it can |
| tell us where are the beats it can allow |
|
|
| align:start position:0% |
| tell us where are the beats it can allow |
| |
|
|
| align:start position:0% |
| tell us where are the beats it can allow |
| us to look at the water and like find |
|
|
| align:start position:0% |
| us to look at the water and like find |
| |
|
|
| align:start position:0% |
| us to look at the water and like find |
| the beats we want to trap so these two |
|
|
| align:start position:0% |
| the beats we want to trap so these two |
| |
|
|
| align:start position:0% |
| the beats we want to trap so these two |
| components in combination are crucial |
|
|
| align:start position:0% |
| components in combination are crucial |
| |
|
|
| align:start position:0% |
| components in combination are crucial |
| for the success of our research there is |
|
|
| align:start position:0% |
| for the success of our research there is |
| |
|
|
| align:start position:0% |
| for the success of our research there is |
| interesting electronics coming behind |
|
|
| align:start position:0% |
| interesting electronics coming behind |
| |
|
|
| align:start position:0% |
| interesting electronics coming behind |
| this essentially the signals from the |
|
|
| align:start position:0% |
| this essentially the signals from the |
| |
|
|
| align:start position:0% |
| this essentially the signals from the |
| QPD and from the stage position where we |
|
|
| align:start position:0% |
| QPD and from the stage position where we |
| |
|
|
| align:start position:0% |
| QPD and from the stage position where we |
| put our sample are |
|
|
| align:start position:0% |
| put our sample are |
| |
|
|
| align:start position:0% |
| put our sample are |
| given in terms of volts so a natural |
|
|
| align:start position:0% |
| given in terms of volts so a natural |
| |
|
|
| align:start position:0% |
| given in terms of volts so a natural |
| question that arises is how are we going |
|
|
| align:start position:0% |
| question that arises is how are we going |
| |
|
|
| align:start position:0% |
| question that arises is how are we going |
| to remember what is important there are |
|
|
| align:start position:0% |
| to remember what is important there are |
| |
|
|
| align:start position:0% |
| to remember what is important there are |
| two important things that would like to |
|
|
| align:start position:0% |
| two important things that would like to |
| |
|
|
| align:start position:0% |
| two important things that would like to |
| keep track of two positions the first |
|
|
| align:start position:0% |
| keep track of two positions the first |
| |
|
|
| align:start position:0% |
| keep track of two positions the first |
| one is the position of the stage that |
|
|
| align:start position:0% |
| one is the position of the stage that |
| |
|
|
| align:start position:0% |
| one is the position of the stage that |
| gives us a relative point of |
|
|
| align:start position:0% |
| gives us a relative point of |
| |
|
|
| align:start position:0% |
| gives us a relative point of |
| consideration and the second one is the |
|
|
| align:start position:0% |
| consideration and the second one is the |
| |
|
|
| align:start position:0% |
| consideration and the second one is the |
| position of the QPD which as you can |
|
|
| align:start position:0% |
| position of the QPD which as you can |
| |
|
|
| align:start position:0% |
| position of the QPD which as you can |
| recall it measures the place of the beat |
|
|
| align:start position:0% |
| recall it measures the place of the beat |
| |
|
|
| align:start position:0% |
| recall it measures the place of the beat |
| that we have trapped these inputs are |
|
|
| align:start position:0% |
| that we have trapped these inputs are |
| |
|
|
| align:start position:0% |
| that we have trapped these inputs are |
| given in terms of volts so the natural |
|
|
| align:start position:0% |
| given in terms of volts so the natural |
| |
|
|
| align:start position:0% |
| given in terms of volts so the natural |
| thing to do is to find a calibration |
|
|
| align:start position:0% |
| thing to do is to find a calibration |
| |
|
|
| align:start position:0% |
| thing to do is to find a calibration |
| that converts these volts into actual |
|
|
| align:start position:0% |
| that converts these volts into actual |
| |
|
|
| align:start position:0% |
| that converts these volts into actual |
| distances here you can see how we do |
|
|
| align:start position:0% |
| distances here you can see how we do |
| |
|
|
| align:start position:0% |
| distances here you can see how we do |
| this we plot the stage X or position you |
|
|
| align:start position:0% |
| this we plot the stage X or position you |
| |
|
|
| align:start position:0% |
| this we plot the stage X or position you |
| can we can plot the stage Y it's |
|
|
| align:start position:0% |
| can we can plot the stage Y it's |
| |
|
|
| align:start position:0% |
| can we can plot the stage Y it's |
| completely analogous to the to the QPD |
|
|
| align:start position:0% |
| completely analogous to the to the QPD |
| |
|
|
| align:start position:0% |
| completely analogous to the to the QPD |
| positions here and the conversion factor |
|
|
| align:start position:0% |
| positions here and the conversion factor |
| |
|
|
| align:start position:0% |
| positions here and the conversion factor |
| hides along these slopes here well as |
|
|
| align:start position:0% |
| hides along these slopes here well as |
| |
|
|
| align:start position:0% |
| hides along these slopes here well as |
| you can see we have two different slopes |
|
|
| align:start position:0% |
| you can see we have two different slopes |
| |
|
|
| align:start position:0% |
| you can see we have two different slopes |
| here with different absolute values so |
|
|
| align:start position:0% |
| here with different absolute values so |
| |
|
|
| align:start position:0% |
| here with different absolute values so |
| this type of measurement is prone to |
|
|
| align:start position:0% |
| this type of measurement is prone to |
| |
|
|
| align:start position:0% |
| this type of measurement is prone to |
| errors how we approach this problem is |
|
|
| align:start position:0% |
| errors how we approach this problem is |
| |
|
|
| align:start position:0% |
| errors how we approach this problem is |
| that we fought by choosing more data |
|
|
| align:start position:0% |
| that we fought by choosing more data |
| |
|
|
| align:start position:0% |
| that we fought by choosing more data |
| points and trying to increase the |
|
|
| align:start position:0% |
| points and trying to increase the |
| |
|
|
| align:start position:0% |
| points and trying to increase the |
| statistic thus hopefully reducing the |
|
|
| align:start position:0% |
| statistic thus hopefully reducing the |
| |
|
|
| align:start position:0% |
| statistic thus hopefully reducing the |
| systematics of this measurement the |
|
|
| align:start position:0% |
| systematics of this measurement the |
| |
|
|
| align:start position:0% |
| systematics of this measurement the |
| second step is to start getting the |
|
|
| align:start position:0% |
| second step is to start getting the |
| |
|
|
| align:start position:0% |
| second step is to start getting the |
| components that we need in order to |
|
|
| align:start position:0% |
| components that we need in order to |
| |
|
|
| align:start position:0% |
| components that we need in order to |
| extract KB is to measure the stiffness |
|
|
| align:start position:0% |
| extract KB is to measure the stiffness |
| |
|
|
| align:start position:0% |
| extract KB is to measure the stiffness |
| coefficient alpha now the main idea is |
|
|
| align:start position:0% |
| coefficient alpha now the main idea is |
| |
|
|
| align:start position:0% |
| coefficient alpha now the main idea is |
| to take the equation of motion and to |
|
|
| align:start position:0% |
| to take the equation of motion and to |
| |
|
|
| align:start position:0% |
| to take the equation of motion and to |
| make a Fourier transform in order to get |
|
|
| align:start position:0% |
| make a Fourier transform in order to get |
| |
|
|
| align:start position:0% |
| make a Fourier transform in order to get |
| the positions in terms of frequencies |
|
|
| align:start position:0% |
| the positions in terms of frequencies |
| |
|
|
| align:start position:0% |
| the positions in terms of frequencies |
| there is mathematics behind this and |
|
|
| align:start position:0% |
| there is mathematics behind this and |
| |
|
|
| align:start position:0% |
| there is mathematics behind this and |
| essentially the power spectral |
|
|
| align:start position:0% |
| essentially the power spectral |
| |
|
|
| align:start position:0% |
| essentially the power spectral |
| distribution and as the distribution of |
|
|
| align:start position:0% |
| distribution and as the distribution of |
| |
|
|
| align:start position:0% |
| distribution and as the distribution of |
| this motion here that we expect obtains |
|
|
| align:start position:0% |
| this motion here that we expect obtains |
| |
|
|
| align:start position:0% |
| this motion here that we expect obtains |
| this form here from where we can extract |
|
|
| align:start position:0% |
| this form here from where we can extract |
| |
|
|
| align:start position:0% |
| this form here from where we can extract |
| the characteristic frequency F naught |
|
|
| align:start position:0% |
| the characteristic frequency F naught |
| |
|
|
| align:start position:0% |
| the characteristic frequency F naught |
| and F naught gives us alpha which is |
|
|
| align:start position:0% |
| and F naught gives us alpha which is |
| |
|
|
| align:start position:0% |
| and F naught gives us alpha which is |
| what we really need this is a log-log |
|
|
| align:start position:0% |
| what we really need this is a log-log |
| |
|
|
| align:start position:0% |
| what we really need this is a log-log |
| plot as you can see here another thing I |
|
|
| align:start position:0% |
| plot as you can see here another thing I |
| |
|
|
| align:start position:0% |
| plot as you can see here another thing I |
| would like to mention is look at the |
|
|
| align:start position:0% |
| would like to mention is look at the |
| |
|
|
| align:start position:0% |
| would like to mention is look at the |
| proportionality here as we increase the |
|
|
| align:start position:0% |
| proportionality here as we increase the |
| |
|
|
| align:start position:0% |
| proportionality here as we increase the |
| power we also increase the stiffness |
|
|
| align:start position:0% |
| power we also increase the stiffness |
| |
|
|
| align:start position:0% |
| power we also increase the stiffness |
| coefficient alpha because we trap more |
|
|
| align:start position:0% |
| coefficient alpha because we trap more |
| |
|
|
| align:start position:0% |
| coefficient alpha because we trap more |
| closely so it means that F nost has to |
|
|
| align:start position:0% |
| closely so it means that F nost has to |
| |
|
|
| align:start position:0% |
| closely so it means that F nost has to |
| increase and indeed when we increase the |
|
|
| align:start position:0% |
| increase and indeed when we increase the |
| |
|
|
| align:start position:0% |
| increase and indeed when we increase the |
| power we are shifting F naught to the |
|
|
| align:start position:0% |
| power we are shifting F naught to the |
| |
|
|
| align:start position:0% |
| power we are shifting F naught to the |
| right having all these components |
|
|
| align:start position:0% |
| right having all these components |
| |
|
|
| align:start position:0% |
| right having all these components |
| we can put this into the big picture and |
|
|
| align:start position:0% |
| we can put this into the big picture and |
| |
|
|
| align:start position:0% |
| we can put this into the big picture and |
| the big picture is the extraction of KB |
|
|
| align:start position:0% |
| the big picture is the extraction of KB |
| |
|
|
| align:start position:0% |
| the big picture is the extraction of KB |
| over here I showed you x squared the |
|
|
| align:start position:0% |
| over here I showed you x squared the |
| |
|
|
| align:start position:0% |
| over here I showed you x squared the |
| fluctuations I showed you alpha we can |
|
|
| align:start position:0% |
| fluctuations I showed you alpha we can |
| |
|
|
| align:start position:0% |
| fluctuations I showed you alpha we can |
| measure the temperature T and then we |
|
|
| align:start position:0% |
| measure the temperature T and then we |
| |
|
|
| align:start position:0% |
| measure the temperature T and then we |
| can get Kb the essence of this |
|
|
| align:start position:0% |
| can get Kb the essence of this |
| |
|
|
| align:start position:0% |
| can get Kb the essence of this |
| measurement is to look at the inverse |
|
|
| align:start position:0% |
| measurement is to look at the inverse |
| |
|
|
| align:start position:0% |
| measurement is to look at the inverse |
| proportionality between fluctuations and |
|
|
| align:start position:0% |
| proportionality between fluctuations and |
| |
|
|
| align:start position:0% |
| proportionality between fluctuations and |
| trap stiffness then we can make a fit |
|
|
| align:start position:0% |
| trap stiffness then we can make a fit |
| |
|
|
| align:start position:0% |
| trap stiffness then we can make a fit |
| with a reasonable chi-square probability |
|
|
| align:start position:0% |
| with a reasonable chi-square probability |
| |
|
|
| align:start position:0% |
| with a reasonable chi-square probability |
| and from here we can extract Kb the |
|
|
| align:start position:0% |
| and from here we can extract Kb the |
| |
|
|
| align:start position:0% |
| and from here we can extract Kb the |
| result is presented on the slide we also |
|
|
| align:start position:0% |
| result is presented on the slide we also |
| |
|
|
| align:start position:0% |
| result is presented on the slide we also |
| show you the measurement that we extract |
|
|
| align:start position:0% |
| show you the measurement that we extract |
| |
|
|
| align:start position:0% |
| show you the measurement that we extract |
| from literature our result is within two |
|
|
| align:start position:0% |
| from literature our result is within two |
| |
|
|
| align:start position:0% |
| from literature our result is within two |
| sigma of the accepted value of KB |
|
|
| align:start position:0% |
| sigma of the accepted value of KB |
| |
|
|
| align:start position:0% |
| sigma of the accepted value of KB |
| actually we're very close to 1 Sigma |
|
|
| align:start position:0% |
| actually we're very close to 1 Sigma |
| |
|
|
| align:start position:0% |
| actually we're very close to 1 Sigma |
| from the accepted value of KB what is |
|
|
| align:start position:0% |
| from the accepted value of KB what is |
| |
|
|
| align:start position:0% |
| from the accepted value of KB what is |
| driving this like unfortunate outcome |
|
|
| align:start position:0% |
| driving this like unfortunate outcome |
| |
|
|
| align:start position:0% |
| driving this like unfortunate outcome |
| the thing that drives this unfortunate |
|
|
| align:start position:0% |
| the thing that drives this unfortunate |
| |
|
|
| align:start position:0% |
| the thing that drives this unfortunate |
| outcome is the systematic errors on our |
|
|
| align:start position:0% |
| outcome is the systematic errors on our |
| |
|
|
| align:start position:0% |
| outcome is the systematic errors on our |
| picture this is our starting error this |
|
|
| align:start position:0% |
| picture this is our starting error this |
| |
|
|
| align:start position:0% |
| picture this is our starting error this |
| is the uncertainty in KB and there are |
|
|
| align:start position:0% |
| is the uncertainty in KB and there are |
| |
|
|
| align:start position:0% |
| is the uncertainty in KB and there are |
| different factors that contribute it to |
|
|
| align:start position:0% |
| different factors that contribute it to |
| |
|
|
| align:start position:0% |
| different factors that contribute it to |
| this as you saw the calibration is very |
|
|
| align:start position:0% |
| this as you saw the calibration is very |
| |
|
|
| align:start position:0% |
| this as you saw the calibration is very |
| difficult |
|
|
| align:start position:0% |
| difficult |
| |
|
|
| align:start position:0% |
| difficult |
| we have error from the laser hitting the |
|
|
| align:start position:0% |
| we have error from the laser hitting the |
| |
|
|
| align:start position:0% |
| we have error from the laser hitting the |
| water and changing the temperature we |
|
|
| align:start position:0% |
| water and changing the temperature we |
| |
|
|
| align:start position:0% |
| water and changing the temperature we |
| have systematic error of the electronics |
|
|
| align:start position:0% |
| have systematic error of the electronics |
| |
|
|
| align:start position:0% |
| have systematic error of the electronics |
| which we safely ignore because the first |
|
|
| align:start position:0% |
| which we safely ignore because the first |
| |
|
|
| align:start position:0% |
| which we safely ignore because the first |
| two factors dominate this our |
|
|
| align:start position:0% |
| two factors dominate this our |
| |
|
|
| align:start position:0% |
| two factors dominate this our |
| electronics were very precise and then |
|
|
| align:start position:0% |
| electronics were very precise and then |
| |
|
|
| align:start position:0% |
| electronics were very precise and then |
| we have the statistical uncertainties |
|
|
| align:start position:0% |
| we have the statistical uncertainties |
| |
|
|
| align:start position:0% |
| we have the statistical uncertainties |
| that we use which correspond to some |
|
|
| align:start position:0% |
| that we use which correspond to some |
| |
|
|
| align:start position:0% |
| that we use which correspond to some |
| error propagating tricks okay now let's |
|
|
| align:start position:0% |
| error propagating tricks okay now let's |
| |
|
|
| align:start position:0% |
| error propagating tricks okay now let's |
| do our investigation the first one is |
|
|
| align:start position:0% |
| do our investigation the first one is |
| |
|
|
| align:start position:0% |
| do our investigation the first one is |
| about the calibration as you can see all |
|
|
| align:start position:0% |
| about the calibration as you can see all |
| |
|
|
| align:start position:0% |
| about the calibration as you can see all |
| of these slopes should be valid but |
|
|
| align:start position:0% |
| of these slopes should be valid but |
| |
|
|
| align:start position:0% |
| of these slopes should be valid but |
| they're actually not so what we do is we |
|
|
| align:start position:0% |
| they're actually not so what we do is we |
| |
|
|
| align:start position:0% |
| they're actually not so what we do is we |
| take them into account we average them |
|
|
| align:start position:0% |
| take them into account we average them |
| |
|
|
| align:start position:0% |
| take them into account we average them |
| then we take more data points we average |
|
|
| align:start position:0% |
| then we take more data points we average |
| |
|
|
| align:start position:0% |
| then we take more data points we average |
| again and then we propagate the errors |
|
|
| align:start position:0% |
| again and then we propagate the errors |
| |
|
|
| align:start position:0% |
| again and then we propagate the errors |
| in order to reduce the systematics the |
|
|
| align:start position:0% |
| in order to reduce the systematics the |
| |
|
|
| align:start position:0% |
| in order to reduce the systematics the |
| second one is due to the heating of the |
|
|
| align:start position:0% |
| second one is due to the heating of the |
| |
|
|
| align:start position:0% |
| second one is due to the heating of the |
| laser essentially what happens is when |
|
|
| align:start position:0% |
| laser essentially what happens is when |
| |
|
|
| align:start position:0% |
| laser essentially what happens is when |
| the laser hits the water it starts |
|
|
| align:start position:0% |
| the laser hits the water it starts |
| |
|
|
| align:start position:0% |
| the laser hits the water it starts |
| heating the vicinity and this is |
|
|
| align:start position:0% |
| heating the vicinity and this is |
| |
|
|
| align:start position:0% |
| heating the vicinity and this is |
| unfortunate because yes we can measure |
|
|
| align:start position:0% |
| unfortunate because yes we can measure |
| |
|
|
| align:start position:0% |
| unfortunate because yes we can measure |
| the room temperature by using the therm |
|
|
| align:start position:0% |
| the room temperature by using the therm |
| |
|
|
| align:start position:0% |
| the room temperature by using the therm |
| but actual uncertainty on the |
|
|
| align:start position:0% |
| but actual uncertainty on the |
| |
|
|
| align:start position:0% |
| but actual uncertainty on the |
| temperature is much bigger because we |
|
|
| align:start position:0% |
| temperature is much bigger because we |
| |
|
|
| align:start position:0% |
| temperature is much bigger because we |
| have extra heating due to the laser we |
|
|
| align:start position:0% |
| have extra heating due to the laser we |
| |
|
|
| align:start position:0% |
| have extra heating due to the laser we |
| tried elegantly to to avoid this by |
|
|
| align:start position:0% |
| tried elegantly to to avoid this by |
| |
|
|
| align:start position:0% |
| tried elegantly to to avoid this by |
| moving the laser constantly so that it |
|
|
| align:start position:0% |
| moving the laser constantly so that it |
| |
|
|
| align:start position:0% |
| moving the laser constantly so that it |
| doesn't stay in one place and heat up a |
|
|
| align:start position:0% |
| doesn't stay in one place and heat up a |
| |
|
|
| align:start position:0% |
| doesn't stay in one place and heat up a |
| lot but it's very hard to quantify how |
|
|
| align:start position:0% |
| lot but it's very hard to quantify how |
| |
|
|
| align:start position:0% |
| lot but it's very hard to quantify how |
| exactly it heats up the water and the |
|
|
| align:start position:0% |
| exactly it heats up the water and the |
| |
|
|
| align:start position:0% |
| exactly it heats up the water and the |
| third one is it's concerned with our fit |
|
|
| align:start position:0% |
| third one is it's concerned with our fit |
| |
|
|
| align:start position:0% |
| third one is it's concerned with our fit |
| with fluctuations in terms of the trap |
|
|
| align:start position:0% |
| with fluctuations in terms of the trap |
| |
|
|
| align:start position:0% |
| with fluctuations in terms of the trap |
| stiffness initially when we did the fit |
|
|
| align:start position:0% |
| stiffness initially when we did the fit |
| |
|
|
| align:start position:0% |
| stiffness initially when we did the fit |
| we with the PhD method we get a |
|
|
| align:start position:0% |
| we with the PhD method we get a |
| |
|
|
| align:start position:0% |
| we with the PhD method we get a |
| probability of chi-square equals 0 and |
|
|
| align:start position:0% |
| probability of chi-square equals 0 and |
| |
|
|
| align:start position:0% |
| probability of chi-square equals 0 and |
| then we quickly realize that essentially |
|
|
| align:start position:0% |
| then we quickly realize that essentially |
| |
|
|
| align:start position:0% |
| then we quickly realize that essentially |
| what we need to do is take into account |
|
|
| align:start position:0% |
| what we need to do is take into account |
| |
|
|
| align:start position:0% |
| what we need to do is take into account |
| the horizontal errors and here what we |
|
|
| align:start position:0% |
| the horizontal errors and here what we |
| |
|
|
| align:start position:0% |
| the horizontal errors and here what we |
| do is we transform the horizontal errors |
|
|
| align:start position:0% |
| do is we transform the horizontal errors |
| |
|
|
| align:start position:0% |
| do is we transform the horizontal errors |
| into the vertical errors and this thing |
|
|
| align:start position:0% |
| into the vertical errors and this thing |
| |
|
|
| align:start position:0% |
| into the vertical errors and this thing |
| we can do by using adding addition in |
|
|
| align:start position:0% |
| we can do by using adding addition in |
| |
|
|
| align:start position:0% |
| we can do by using adding addition in |
| quadrature and propagation of the errors |
|
|
| align:start position:0% |
| quadrature and propagation of the errors |
| |
|
|
| align:start position:0% |
| quadrature and propagation of the errors |
| which gave us a reasonable realistic |
|
|
| align:start position:0% |
| which gave us a reasonable realistic |
| |
|
|
| align:start position:0% |
| which gave us a reasonable realistic |
| chi-squared of 0.33 in conclusion I'll |
|
|
| align:start position:0% |
| chi-squared of 0.33 in conclusion I'll |
| |
|
|
| align:start position:0% |
| chi-squared of 0.33 in conclusion I'll |
| start with limitations as you saw it's |
|
|
| align:start position:0% |
| start with limitations as you saw it's |
| |
|
|
| align:start position:0% |
| start with limitations as you saw it's |
| very hard to distinguish between |
|
|
| align:start position:0% |
| very hard to distinguish between |
| |
|
|
| align:start position:0% |
| very hard to distinguish between |
| systematic errors and statistical |
|
|
| align:start position:0% |
| systematic errors and statistical |
| |
|
|
| align:start position:0% |
| systematic errors and statistical |
| uncertainties the reason for this is as |
|
|
| align:start position:0% |
| uncertainties the reason for this is as |
| |
|
|
| align:start position:0% |
| uncertainties the reason for this is as |
| you saw is that we are fighting with the |
|
|
| align:start position:0% |
| you saw is that we are fighting with the |
| |
|
|
| align:start position:0% |
| you saw is that we are fighting with the |
| systematics by introducing more |
|
|
| align:start position:0% |
| systematics by introducing more |
| |
|
|
| align:start position:0% |
| systematics by introducing more |
| statistics and everything mixes up in |
|
|
| align:start position:0% |
| statistics and everything mixes up in |
| |
|
|
| align:start position:0% |
| statistics and everything mixes up in |
| the propagation of errors the second |
|
|
| align:start position:0% |
| the propagation of errors the second |
| |
|
|
| align:start position:0% |
| the propagation of errors the second |
| thing that it was very difficult in this |
|
|
| align:start position:0% |
| thing that it was very difficult in this |
| |
|
|
| align:start position:0% |
| thing that it was very difficult in this |
| lab is that we need to move the laser |
|
|
| align:start position:0% |
| lab is that we need to move the laser |
| |
|
|
| align:start position:0% |
| lab is that we need to move the laser |
| constantly so one of the one of the |
|
|
| align:start position:0% |
| constantly so one of the one of the |
| |
|
|
| align:start position:0% |
| constantly so one of the one of the |
| people working on this topic has to keep |
|
|
| align:start position:0% |
| people working on this topic has to keep |
| |
|
|
| align:start position:0% |
| people working on this topic has to keep |
| track of where the laser is and whether |
|
|
| align:start position:0% |
| track of where the laser is and whether |
| |
|
|
| align:start position:0% |
| track of where the laser is and whether |
| you're trapping things that you may not |
|
|
| align:start position:0% |
| you're trapping things that you may not |
| |
|
|
| align:start position:0% |
| you're trapping things that you may not |
| want to trap the third thing is to the |
|
|
| align:start position:0% |
| want to trap the third thing is to the |
| |
|
|
| align:start position:0% |
| want to trap the third thing is to the |
| need to find better ways of calibration |
|
|
| align:start position:0% |
| need to find better ways of calibration |
| |
|
|
| align:start position:0% |
| need to find better ways of calibration |
| and there are people who are actively |
|
|
| align:start position:0% |
| and there are people who are actively |
| |
|
|
| align:start position:0% |
| and there are people who are actively |
| working on this on this topic here as |
|
|
| align:start position:0% |
| working on this on this topic here as |
| |
|
|
| align:start position:0% |
| working on this on this topic here as |
| you saw the main source of error came |
|
|
| align:start position:0% |
| you saw the main source of error came |
| |
|
|
| align:start position:0% |
| you saw the main source of error came |
| from the calibration actually but the |
|
|
| align:start position:0% |
| from the calibration actually but the |
| |
|
|
| align:start position:0% |
| from the calibration actually but the |
| process is that we can give a reasonable |
|
|
| align:start position:0% |
| process is that we can give a reasonable |
| |
|
|
| align:start position:0% |
| process is that we can give a reasonable |
| estimate to the Boltzmann constant and |
|
|
| align:start position:0% |
| estimate to the Boltzmann constant and |
| |
|
|
| align:start position:0% |
| estimate to the Boltzmann constant and |
| at the same time we can have a lot of |
|
|
| align:start position:0% |
| at the same time we can have a lot of |
| |
|
|
| align:start position:0% |
| at the same time we can have a lot of |
| fun while doing so I would like to thank |
|
|
| align:start position:0% |
| fun while doing so I would like to thank |
| |
|
|
| align:start position:0% |
| fun while doing so I would like to thank |
| to my partner Emma and I think |
|
|
| align:start position:0% |
| to my partner Emma and I think |
| |
|
|
| align:start position:0% |
| to my partner Emma and I think |
| collaboration is very important for |
|
|
| align:start position:0% |
| collaboration is very important for |
| |
|
|
| align:start position:0% |
| collaboration is very important for |
| Jayla and more specifically for this |
|
|
| align:start position:0% |
| Jayla and more specifically for this |
| |
|
|
| align:start position:0% |
| Jayla and more specifically for this |
| particular experiment this experiment is |
|
|
| align:start position:0% |
| particular experiment this experiment is |
| |
|
|
| align:start position:0% |
| particular experiment this experiment is |
| impossible to be done without a partner |
|
|
| align:start position:0% |
| impossible to be done without a partner |
| |
|
|
| align:start position:0% |
| impossible to be done without a partner |
| because it's very difficult it's very |
|
|
| align:start position:0% |
| because it's very difficult it's very |
| |
|
|
| align:start position:0% |
| because it's very difficult it's very |
| difficult to keep track of where you |
|
|
| align:start position:0% |
| difficult to keep track of where you |
| |
|
|
| align:start position:0% |
| difficult to keep track of where you |
| want to put |
|
|
| align:start position:0% |
| want to put |
| |
|
|
| align:start position:0% |
| want to put |
| and also what is going on around the |
|
|
| align:start position:0% |
| and also what is going on around the |
| |
|
|
| align:start position:0% |
| and also what is going on around the |
| laser well one of the people who is |
|
|
| align:start position:0% |
| laser well one of the people who is |
| |
|
|
| align:start position:0% |
| laser well one of the people who is |
| moving the laser the other one should be |
|
|
| align:start position:0% |
| moving the laser the other one should be |
| |
|
|
| align:start position:0% |
| moving the laser the other one should be |
| looking looking at the CCD camera and |
|
|
| align:start position:0% |
| looking looking at the CCD camera and |
| |
|
|
| align:start position:0% |
| looking looking at the CCD camera and |
| like telling where are we going on like |
|
|
| align:start position:0% |
| like telling where are we going on like |
| |
|
|
| align:start position:0% |
| like telling where are we going on like |
| what are we actually trapping like what |
|
|
| align:start position:0% |
| what are we actually trapping like what |
| |
|
|
| align:start position:0% |
| what are we actually trapping like what |
| do we want to avoid like we don't want |
|
|
| align:start position:0% |
| do we want to avoid like we don't want |
| |
|
|
| align:start position:0% |
| do we want to avoid like we don't want |
| these guys in our picture I also like to |
|
|
| align:start position:0% |
| these guys in our picture I also like to |
| |
|
|
| align:start position:0% |
| these guys in our picture I also like to |
| thank the staff of this class for their |
|
|
| align:start position:0% |
| thank the staff of this class for their |
| |
|
|
| align:start position:0% |
| thank the staff of this class for their |
| useful feedback and their valuable help |
|
|
| align:start position:0% |
| useful feedback and their valuable help |
| |
|
|
| align:start position:0% |
| useful feedback and their valuable help |
| and finally for your attention yeah so |
|
|
| align:start position:0% |
| and finally for your attention yeah so |
| |
|
|
| align:start position:0% |
| and finally for your attention yeah so |
| we have a lot of this should be trap |
|
|
| align:start position:0% |
| we have a lot of this should be trap |
| |
|
|
| align:start position:0% |
| we have a lot of this should be trap |
| stiffness versus the this is the current |
|
|
| align:start position:0% |
| stiffness versus the this is the current |
| |
|
|
| align:start position:0% |
| stiffness versus the this is the current |
| and here actually I haven't shown that |
|
|
| align:start position:0% |
| and here actually I haven't shown that |
| |
|
|
| align:start position:0% |
| and here actually I haven't shown that |
| it's like the trap stiffness defers |
|
|
| align:start position:0% |
| it's like the trap stiffness defers |
| |
|
|
| align:start position:0% |
| it's like the trap stiffness defers |
| whether you look in the X direction or |
|
|
| align:start position:0% |
| whether you look in the X direction or |
| |
|
|
| align:start position:0% |
| whether you look in the X direction or |
| the Y direction the actual measurements |
|
|
| align:start position:0% |
| the Y direction the actual measurements |
| |
|
|
| align:start position:0% |
| the Y direction the actual measurements |
| are analog is because the mathematics is |
|
|
| align:start position:0% |
| are analog is because the mathematics is |
| |
|
|
| align:start position:0% |
| are analog is because the mathematics is |
| the same but as you can see here we have |
|
|
| align:start position:0% |
| the same but as you can see here we have |
| |
|
|
| align:start position:0% |
| the same but as you can see here we have |
| different data points for the two cases |
|
|
| align:start position:0% |
| different data points for the two cases |
| |
|
|
| align:start position:0% |
| different data points for the two cases |
| we account this into our considerations |
|
|
| align:start position:0% |
| we account this into our considerations |
| |
|
|
| align:start position:0% |
| we account this into our considerations |
| yes yes |
|
|
| align:start position:0% |
| |
| |
|
|
| align:start position:0% |
| |
| mmm |
|
|
| align:start position:0% |
| |
| |
|
|
| align:start position:0% |
| |
| well I mean the air case well I mean |
|
|
| align:start position:0% |
| well I mean the air case well I mean |
| |
|
|
| align:start position:0% |
| well I mean the air case well I mean |
| everything boils down to this this |
|
|
| align:start position:0% |
| everything boils down to this this |
| |
|
|
| align:start position:0% |
| everything boils down to this this |
| consideration here okay let me just find |
|
|
| align:start position:0% |
| consideration here okay let me just find |
| |
|
|
| align:start position:0% |
| consideration here okay let me just find |
| my explanation it boils down to the the |
|
|
| align:start position:0% |
| my explanation it boils down to the the |
| |
|
|
| align:start position:0% |
| my explanation it boils down to the the |
| viscosity that dominates so in our case |
|
|
| align:start position:0% |
| viscosity that dominates so in our case |
| |
|
|
| align:start position:0% |
| viscosity that dominates so in our case |
| we have the viscosity of water that |
|
|
| align:start position:0% |
| we have the viscosity of water that |
| |
|
|
| align:start position:0% |
| we have the viscosity of water that |
| dominates when you look in different |
|
|
| align:start position:0% |
| dominates when you look in different |
| |
|
|
| align:start position:0% |
| dominates when you look in different |
| mediums you might have different types |
|
|
| align:start position:0% |
| mediums you might have different types |
| |
|
|
| align:start position:0% |
| mediums you might have different types |
| of viscosity which would change the |
|
|
| align:start position:0% |
| of viscosity which would change the |
| |
|
|
| align:start position:0% |
| of viscosity which would change the |
| motions so I have the paper I I didn't |
|
|
| align:start position:0% |
| motions so I have the paper I I didn't |
| |
|
|
| align:start position:0% |
| motions so I have the paper I I didn't |
| actually read through the whole details |
|
|
| align:start position:0% |
| actually read through the whole details |
| |
|
|
| align:start position:0% |
| actually read through the whole details |
| of the how exactly the mathematics |
|
|
| align:start position:0% |
| of the how exactly the mathematics |
| |
|
|
| align:start position:0% |
| of the how exactly the mathematics |
| changes probably does also probably and |
|
|
| align:start position:0% |
| changes probably does also probably and |
| |
|
|
| align:start position:0% |
| changes probably does also probably and |
| other issues that are that may not arise |
|
|
| align:start position:0% |
| other issues that are that may not arise |
| |
|
|
| align:start position:0% |
| other issues that are that may not arise |
| or may arise is the laser like in this |
|
|
| align:start position:0% |
| or may arise is the laser like in this |
| |
|
|
| align:start position:0% |
| or may arise is the laser like in this |
| case like laser like heats up the the |
|
|
| align:start position:0% |
| case like laser like heats up the the |
| |
|
|
| align:start position:0% |
| case like laser like heats up the the |
| water but I don't know how exactly the |
|
|
| align:start position:0% |
| water but I don't know how exactly the |
| |
|
|
| align:start position:0% |
| water but I don't know how exactly the |
| laser would react with the air maybe |
|
|
| align:start position:0% |
| laser would react with the air maybe |
| |
|
|
| align:start position:0% |
| laser would react with the air maybe |
| it's going to heat up a little bit but |
|
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| align:start position:0% |
| it's going to heat up a little bit but |
| |
|
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| align:start position:0% |
| it's going to heat up a little bit but |
| how is this heat by going to be |
|
|
| align:start position:0% |
| how is this heat by going to be |
| |
|
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| align:start position:0% |
| how is this heat by going to be |
| distributed in space I'm not very |
|
|
| align:start position:0% |
| distributed in space I'm not very |
| |
|
|
| align:start position:0% |
| distributed in space I'm not very |
| knowledgeable of this as it now |
|
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| align:start position:0% |
| |
| |
|
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| align:start position:0% |
| |
| so the equipartition theorem it breaks |
|
|
| align:start position:0% |
| so the equipartition theorem it breaks |
| |
|
|
| align:start position:0% |
| so the equipartition theorem it breaks |
| into components it breaks into the |
|
|
| align:start position:0% |
| into components it breaks into the |
| |
|
|
| align:start position:0% |
| into components it breaks into the |
| component of X where we have one degree |
|
|
| align:start position:0% |
| component of X where we have one degree |
| |
|
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| align:start position:0% |
| component of X where we have one degree |
| of freedom and it breaks into the |
|
|
| align:start position:0% |
| of freedom and it breaks into the |
| |
|
|
| align:start position:0% |
| of freedom and it breaks into the |
| component of Y where have another degree |
|
|
| align:start position:0% |
| component of Y where have another degree |
| |
|
|
| align:start position:0% |
| component of Y where have another degree |
| of freedom |
|
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| align:start position:0% |
| of freedom |
| |
|
|
| align:start position:0% |
| of freedom |
| each of these considerations is |
|
|
| align:start position:0% |
| each of these considerations is |
| |
|
|
| align:start position:0% |
| each of these considerations is |
| concerned only with in one movement so |
|
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| align:start position:0% |
| concerned only with in one movement so |
| |
|
|
| align:start position:0% |
| concerned only with in one movement so |
| for the okay well you can think about it |
|
|
| align:start position:0% |
| for the okay well you can think about it |
| |
|
|
| align:start position:0% |
| for the okay well you can think about it |
| in this way we have two degrees of |
|
|
| align:start position:0% |
| in this way we have two degrees of |
| |
|
|
| align:start position:0% |
| in this way we have two degrees of |
| freedom in total but in the actual |
|
|
| align:start position:0% |
| freedom in total but in the actual |
| |
|
|
| align:start position:0% |
| freedom in total but in the actual |
| directions that are useful for our |
|
|
| align:start position:0% |
| directions that are useful for our |
| |
|
|
| align:start position:0% |
| directions that are useful for our |
| considerations we have only one degree |
|
|
| align:start position:0% |
| considerations we have only one degree |
| |
|
|
| align:start position:0% |
| considerations we have only one degree |
| of freedom so yeah well I think this is |
|
|
| align:start position:0% |
| of freedom so yeah well I think this is |
| |
|
|
| align:start position:0% |
| of freedom so yeah well I think this is |
| for this this is 3.2 microns and this |
|
|
| align:start position:0% |
| for this this is 3.2 microns and this |
| |
|
|
| align:start position:0% |
| for this this is 3.2 microns and this |
| like later on like you might you saw the |
|
|
| align:start position:0% |
| like later on like you might you saw the |
| |
|
|
| align:start position:0% |
| like later on like you might you saw the |
| 1 microns |
|
|
| align:start position:0% |
| 1 microns |
| |
|
|
| align:start position:0% |
| 1 microns |
| I think our data is concerned with the |
|
|
| align:start position:0% |
| I think our data is concerned with the |
| |
|
|
| align:start position:0% |
| I think our data is concerned with the |
| 3.2 microns we didn't I like my results |
|
|
| align:start position:0% |
| 3.2 microns we didn't I like my results |
| |
|
|
| align:start position:0% |
| 3.2 microns we didn't I like my results |
| are not related with the micron 1 micron |
|
|
| align:start position:0% |
| are not related with the micron 1 micron |
| |
|
|
| align:start position:0% |
| are not related with the micron 1 micron |
| we just played with it and try this we |
|
|
| align:start position:0% |
| we just played with it and try this we |
| |
|
|
| align:start position:0% |
| we just played with it and try this we |
| also tried the trapping cells from |
|
|
| align:start position:0% |
| also tried the trapping cells from |
| |
|
|
| align:start position:0% |
| also tried the trapping cells from |
| onions it was very fun to play with but |
|
|
| align:start position:0% |
| onions it was very fun to play with but |
| |
|
|
| align:start position:0% |
| onions it was very fun to play with but |
| unfortunately we couldn't get any like |
|
|
| align:start position:0% |
| unfortunately we couldn't get any like |
| |
|
|
| align:start position:0% |
| unfortunately we couldn't get any like |
| valuable quantitative results there so |
|
|
| align:start position:0% |
| valuable quantitative results there so |
| |
|
|
| align:start position:0% |
| valuable quantitative results there so |
| even though it's quite a lot of fun we |
|
|
| align:start position:0% |
| even though it's quite a lot of fun we |
| |
|
|
| align:start position:0% |
| even though it's quite a lot of fun we |
| have some clips it's not worth for this |
|
|
| align:start position:0% |
| have some clips it's not worth for this |
| |
|
|
| align:start position:0% |
| have some clips it's not worth for this |
| presentation which concentrates on the |
|
|
| align:start position:0% |
| presentation which concentrates on the |
| |
|
|
| align:start position:0% |
| presentation which concentrates on the |
| KB |
|
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| align:start position:0% |
| |
| |
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| align:start position:0% |
| |
| [Applause] |
