Method for obtaining the absorption position, mass and rigidity of a particle
AssigneesNanodreams, S.L., Consejo Superior de Investigaciones Cientificas
InventorsOscar Malvar Vidal, Jose Jaime Ruz Martinez, Priscila Monteiro Kosaka, Montserrat Calleja Gomez, Francisco Javier Tamayo De Miguel
Life of this patent
Estimating the term…
Abstract
A method for obtaining the absorption position, mass and rigidity of a particle deposited on the surface of a resonator based on the relative change in the resonance frequency of said resonator in 3 or 4 flexural vibration modes. The rigidity of the particles is of great interest in the study of cells and other biological compounds that change state without significantly changing the mass.
Claims13
1-5. (canceled)
A method for obtaining the absorption position, mass and rigidity of a particle deposited on the surface of a resonator based on the relative change in the resonance frequency of said resonator in N=3 or N=4 flexural vibration modes, where said method comprises the following steps:
- a. the standard deviation of the relative frequency change of each mode σn and the values of the relative frequency change corresponding to adsorption μn is calculated,
- b. the following probability density function is formed
- JPDF
-
- (
- Ω
- ^
- )
- =
- e
- -
- (
- Ω
- ^
- -
- M
- )
-
- Σ
- -
- 1
-
- (
- Ω
- ^
- -
- M
- )
- T
- 2
- (
- 2
-
-
- π
- )
- N
- /
- 2
-
-
- Σ
-
- where {circumflex over (Ω)}=(Ω1,Ω2, . . . , ΩN), with Ωn given by:
- Ω
- n
- =
- -
- Δ
- m
-
- ψ
- n
-
- (
- ξ
- 0
- )
- 2
- +
- Δ
- s
-
- 1
- β
- n
- 4
-
- (
- d
- 2
-
- ψ
- n
-
- (
- ξ
- 0
- )
- d
-
-
- ξ
- 2
- )
- 2
- where ψn and βn are the type of vibration and the eigenvalue of the n-th mode, respectively, M=(μ1, μ2, . . . , μN) and Σ is the covariance matrix given by:
- Σ
- =
- (
- σ
- 1
- 2
- σ
- 1
-
- σ
- 2
-
- ρ
- 12
- …
- σ
- 1
-
- σ
- N
-
- ρ
- 1
-
-
- N
- σ
- 1
-
- σ
- 2
-
- ρ
- 12
- σ
- 2
- 2
- …
- ⋮
- ⋮
- ⋮
- ⋱
- ⋮
- σ
- 1
-
- σ
- N
-
- ρ
- 1
-
-
- N
- …
- …
- σ
- N
- 2
- )
- where ρi,j is the correlation between modes i and j;
- c. the values of the absorption position ξ0, the mass term Δm and the rigidity term Δs that maximise the probability density function are calculated.
Dependencies are inferred from the claim text.