Hard topological <i>versus</i> soft geometrical magnetic particle transport

Rossi, Anna M. E. B.; Bugase, Jonas; Lachner, Thomas; Ernst, Adrian; Heras, Daniel de las; Fischer, Thomas M.

doi:10.1039/c9sm01401b

Cited by 7 publications

(7 citation statements)

References 26 publications

(37 reference statements)

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“…Brownian diffusion does not play any role in our system since the external energy is very large compared to the thermal energy. Hence, it would be possible to construct a macroscopic analog of the system using e.g., an arrangement of NbB-magnets 30 . Downscaling the system from the meso-to the nanoscale is challenging since thermal fluctuations might play a role, broadening the fences and facilitating therefore ratchets.…”

Section: Discussionmentioning

confidence: 99%

Simultaneous polydirectional transport of colloidal bipeds

et al. 2020

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Detailed control over the motion of colloidal particles is relevant in many applications in colloidal science such as lab-on-a-chip devices. Here, we use an external magnetic field to assemble paramagnetic colloidal spheres into colloidal rods of several lengths. The rods reside above a square magnetic pattern and are transported via modulation of the direction of the external magnetic field. The rods behave like bipeds walking above the pattern. Depending on their length, the bipeds perform topologically distinct classes of protected walks. We design parallel polydirectional modulation loops of the external field that command up to six classes of bipeds to walk on distinct predesigned paths. Using such loops, we induce the collision of reactant bipeds, their polymerization addition reaction to larger bipeds, the separation of product bipeds from the educts, the sorting of different product bipeds, and also the parallel writing of a word consisting of several letters. Our ideas and methodology might be transferred to other systems for which topological protection is at work.

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Section: Discussionmentioning

confidence: 99%

Simultaneous polydirectional transport of colloidal bipeds

et al. 2020

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“…The famous LMBWequation was derived independently by Lovett, Mou, and Buff [10] and by Wertheim [11] and reads ∇ ln ρ(r) + β∇V ext (r) = dr c 2 (r, r )∇ ρ(r ). (47) We can conclude that (47) is a combination of the local internal Noether sum rule (7) for translational symmetry and the equilibrium Euler-Lagrange equation c 1 (r) = ln ρ(r) + β∇V ext (r) − βµ, where µ indicates the chemical potential. LMBW also derived a lesser known external relation, which is equivalent to (47) and reads…”

Section: Relationship To Classical Resultsmentioning

confidence: 87%

“…Although (50) has a similar structure as the LMBW equation, it is not based on symmetry or Noether arguments but arises from integration out of degrees of freedom. If one would like to include the translational symmetry one can simply replace the left hand side of ( 50) with the right hand side of the LMBW equation (47), which leads to…”

Section: Relationship To Classical Resultsmentioning

confidence: 99%

“…Much of very current attention in Statistical Physics is devoted to nonequilibrium and active systems that are driven in a controlled way out of equilibrium, such as e.g. active Brownian particles [42][43][44] and magnetically controlled topological transport of colloids [45][46][47]. The power functional (variational) theory [48] (PFT) offers to obtain a unifying perspective on nonequilibrium problems such as the above.…”

Section: Introductionmentioning

confidence: 99%

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Noether's Theorem in Statistical Mechanics

Hermann,

Schmidt

2021

Preprint

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We apply Noether's calculus of invariant variations to equilibrium and driven many-body systems. Generating functionals, such as the free energy, yield mechanical laws under continuous translational and rotational symmetry operations. The resulting global theorems express vanishing of total internal and total external forces and torques. Local sum rules interrelate density correlators, as well as static and time direct correlation functions via infinite hierarchies, including memory. For anisotropic particles, systematic coupling of orbital and spin motion is identified. The theory allows to shed new light on the spatio-temporal coupling of correlations in complex systems. When applied to active Brownian particles, the theorem clarifies the role of interfacial forces in motility-induced phase separation. For active sedimentation under gravity the global internal Noether sum rule constrains the motion of the center of mass.

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“…In contrast our biomimetic colloidal trains are driven by the shape of the potential created by the pattern and the external field which creates the topological nature of this classical non-adiabatic phenomenon. We have shown in references [8,9,[16][17][18][19][20] that, like other classical topological transport phenomena [21][22][23][24][25][26][27], there exist similarities with quantum mechanical topological transport [28,29].…”

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confidence: 99%

Colloidal trains

et al. 2020

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Single and double paramagnetic colloidal particles are placed above a magnetic square pattern and are driven with an external magnetic field precessing around a high symmetry direction of the pattern. The external magnetic field and that of the pattern confine the colloids into lanes parallel to a lattice vector of the pattern. The precession of the external field causes traveling minima of the magnetic potential along the direction of the lanes. At sufficiently high frequencies of modulation only the doublets respond to the external field and move in direction of the traveling minima along the lanes, while the single colloids cannot follow and remain static. We show how the doublets can induce a coordinated motion of the single colloids building colloidal trains made of a chain of several single colloids transported by doublets.

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Hard topological versus soft geometrical magnetic particle transport

Abstract: Geometrical displacement of transported ferrofluid droplets (red) versus topological displacement of transported doublets and single spheres.

Cited by 7 publications

References 26 publications

Simultaneous polydirectional transport of colloidal bipeds

Simultaneous polydirectional transport of colloidal bipeds

Noether's Theorem in Statistical Mechanics

Colloidal trains

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