Dataset for "Metachronal coordination as a mesoscale phenomenon"

Experimental dataset 1: Rotation speed of the device under 1-arm protocol inducing rotation as a function of frequency 

Description: 

This dataset contains experimental measurements of the rotation speed of a 7-bead magnetocapillary device under 1-arm metachronal coordination. The data corresponds to Figure 7(a) of the manuscript. It includes the rotation speed of the device measured at various actuation frequencies, along with the respective standard errors.

Columns:

• Frequency (Hz): Driving frequency
• Rotation speed (rad/s): Average rotation speed.

Experimental dataset 2: Total speed of the swimmer under 2-arm protocol inducing swimming as a function of frequency 

Description: 

This dataset contains experimental measurements of the total speed of a 7-bead magnetocapillary swimmer under 2-arm metachronal coordination. The data corresponds to Figure 7(b) of the manuscript. It includes the total speed of the device measured at various actuation frequencies, along with the respective standard errors.

Columns:

• Frequency (Hz): Driving frequency
• Total speed (bead diameter/s (500 μm/s)): Average total speed.

Experimental dataset 3: Equilibrium distance for static assembly as a function of vertical field

Description: 

This dataset contains nexperimental measurements of the equilibrium distance of a 7-bead magnetocapillary swimmer under the vertical magnetic field only.
These data correspond to Figure 3 in the manuscript.

Columns:

• Vertical field (mT): Constant vertical magnetic field
• Equilibrium distance (mm) without inertia: Average distance between each side 500 μm bead and the central 800 μm bead.

Numerical dataset 1: Rotation speed of the device under 1-arm protocol inducing rotation as a function of frequency 

Description: 

This dataset contains numerical measurements of the rotation speed of a 7-bead magnetocapillary device under 1-arm metachronal coordination. The data corresponds to Figure 7(a) of the manuscript. It includes the rotation speed of the device measured at various actuation frequencies for three different values of the vertical depth parameter: z1= 165, 200, and 220 μm. 

Columns:

• Frequency (Hz): Driving frequency
• Rotation speed (rad/s) for z1=165 μm: Average rotation speed.
• Rotation speed (rad/s) for z1=200 μm: Average rotation speed.
• Rotation speed (rad/s) for z1=220 μm: Average rotation speed.

Numerical dataset 2: Total speed of the device under 2-arm protocol inducing swimming as a function of frequency 

Description: 

This dataset contains numerical measurements of the total speed of a 7-bead magnetocapillary swimmer under 2-arm metachronal coordination. The data corresponds to Figure 7(b) of the manuscript. It includes the total speed of the device measured at various actuation frequencies for a fixed value of the vertical depth parameter: z1= 165 μm. 

Columns:

• Frequency (Hz): Driving frequency
• Total speed (μm/s) for z1=165 μm: Average total speed.

Numerical dataset 3: Constrained simulations: Rotation speed under 1-arm protocol with no individual rotation and no deformation

Description: 

This dataset contains numerical measurements of the rotation speed (in rad/s) of a 7-bead magnetocapillary device under 1-arm metachronal coordination and under constrained conditions. Two scenarios are explored: individual rotation is suppressed (no bead rotation allowed), and deformation is suppressed. The value of z1 is fixed to 200 μm.
These data correspond to Figure 8(a) in the manuscript. 

Columns:

• Frequency (Hz): Driving frequency
• Rotation speed (rad/s) without rotation: Average rotation speed.
• Rotation speed (rad/s) without deformation: Average rotation speed.

Numerical dataset 4: Constrained simulations: Total speed under 2-arm protocol with no individual rotation and no deformation

Description: 

This dataset contains numerical measurements of the total speed (in μm/s) of a 7-bead magnetocapillary swimmer under 2-arm metachronal coordination and under constrained conditions. Two scenarios are explored: individual rotation is suppressed (no bead rotation allowed), and deformation is suppressed. The value of z1 is fixed to 165 μm.
These data correspond to Figure 8(b) in the manuscript.

Columns:

• Frequency (Hz): Driving frequency
• Total speed (μm/s) without rotation: Average total speed.
• Total speed (μm/s) without deformation: Average total speed.

Numerical dataset 5: Constrained simulations: Rotation speed under 1-arm protocol with no inertia

Description: 

This dataset contains numerical measurements of the rotation speed (in rad/s) of a 7-bead magnetocapillary device under 1-arm metachronal coordination and under no inertia conditions (m=0). The value of z1 is fixed to 220 μm.
These data correspond to Figure 10(a) in the manuscript. 

Columns:

• Frequency (Hz): Driving frequency
• Rotation speed (rad/s) without inertia: Average rotation speed.

Numerical dataset 6: Constrained simulations: Total speed under 2-arm protocol with no inertia

Description: 

This dataset contains numerical measurements of the total speed (in μm/s) of a 7-bead magnetocapillary swimmer under 2-arm metachronal coordination and under no inertia conditions (m=0). The value of z1 is fixed to 165 μm.
These data correspond to Figure 10(b) in the manuscript.

Columns:

• Frequency (Hz): Driving frequency
• Total speed (μm/s) without inertia: Average total speed.

Numerical dataset 7: Equilibrium distance for static assembly as a function of vertical field

Description: 

This dataset contains numerical measurements of the equilibrium distance of a 7-bead magnetocapillary swimmer under the vertical magnetic field only for different values of vertical depth parameters z1= 135,175, 220 μm.
These data correspond to Figure 3 in the manuscript.

Columns:

• Vertical field (mT): Constant vertical magnetic field
• Equilibrium distance (mm) without inertia: Average distance between each side 500 μm bead and the central 800 μm bead.

Movie 1: Metachronal coordination under 1-arm protocol inducing rotation

Description:
This movie shows the magnetocapillary assembly driven by the 1-arm metachronal magnetic field protocol at a frequency of f = 1.5 Hz. The assembly exhibits collective rotation. The vertical magnetic field is 4.9 mT, and the horizontal field is 0.74 mT.

Movie 2: Metachronal coordination under 2-arm protocol inducing swimming

Description:
This movie shows the magnetocapillary assembly driven by the 2-arm metachronal magnetic field protocol at a frequency of f = 1.5 Hz. The assembly exhibits collective translation.  The vertical magnetic field is 4.9 mT, and the horizontal field is 1.2 mT.