Dynamics of interacting particle systems: Modeling implications of the repulsive interactions and experiments on magnetic prototypes

Gonella, Stefano

doi:10.1103/physrevb.102.054304

Cited by 6 publications

(2 citation statements)

References 19 publications

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“…To mimic the weak inter-layer interactions, we can resort to pairs of magnets placed at corresponding lattice sites on adjacent layers. While magnets have been used in phononics applications, either as particles of discrete lattices [22], or as a tool to endow structural lattices with programmable nodal mass [23] or to promote multistability [24], their use as a source of inter-layer interaction is less charted. In principle, an arrangement of two structural layers featuring nodal interaction should fully capture the morphology and kinetics of a graphene bilayer.…”

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confidence: 99%

Tunable band gaps and symmetry breaking in magnetomechanical metastructures inspired by multilayer two-dimensional materials

Gonella

2021

Phys. Rev. B

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In this Letter, we introduce a paradigm to realize magneto-mechanical metastructures inspired by multi-layer 2D materials, such as graphene bilayers. The metastructures are intended to capture two aspects of their nanoscale counterparts. One is the multi-layer geometry, which is implemented by stacking hexagonal lattice sheets. The other is the landscape of weak inter-layer forces, which is mimicked by the interactions between pairs of magnets located at corresponding lattice sites on adjacent layers. We illustrate the potential of this paradigm through a three-layer prototype. The two rigid outer lattices serve as control layers, while the thin inner layer is free to experience flexural motion under the confining action of the magnetic forces exchanged with the outer ones, thus behaving as a lattice on elastic foundation. The inner layer is free to rotate relatively to the others, giving rise to a rich spectrum of inter-layer interaction patterns. Our objective is to determine how the dynamical response can be tuned by changing the twist angle between the layers. Specifically, we demonstrate experimentally that switching between different stacking patterns has profound consequences on the phonon landscape, opening and closing bandgaps in different frequency regimes.

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Tunable band gaps and symmetry breaking in magnetomechanical metastructures inspired by multilayer two-dimensional materials

Gonella

2021

Phys. Rev. B

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“…Each disk has two degrees of freedom in the x and y directions. The dispersion relation of the system can be calculated using Bloch's theorem [29] as: [−ω 2 M + K(κ)]φ = 0, where ω is the frequency, κ is the wavenumber, φ = [u v] T is the Bloch displacement vector in the x and y directions, M is the mass matrix, and K(κ) is the stiffness matrix [30], taking into consideration the static repulsive forces between the disks in the equilibrium configuration [31] (See Supp. Mat.).…”

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Exploiting Localized Transition Waves to Tune Sound Propagation in Soft Materials

Watkins,

Eichelberg,

Bilal

2021

Preprint

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Programmable materials hold great potential for many applications such as deployable structures, soft robotics, and wave control, however, the presence of instability and disorder might hinder their utilization. Through a combination of analytical, numerical, and experimental analyses, we harness the interplay between instabilities, geometric frustration, and mechanical deformations to control the propagation of sound waves within self-assembled soft materials. We consider levitated magnetic disks confined by a magnetic boundary inplane. The assemblies can be either ordered or disordered depending on the intrinsic disk symmetry. By applying an external load to the assembly, we observe the nucleation and propagation of different topological defects within the lattices. In the presence of instabilities, the defect propagation gives rise to time-independent localized transition waves. Surprisingly, in the presence of frustration, the applied load briefly introduces deformationinduced order to the material. By further deforming the lattices, new patterns emerge across all disk symmetries. We utilize these patterns to tune sound propagation through the material. Our findings could open new possibilities for designing exotic materials with potential applications ranging from sound control to soft robotics.

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An assessment of the contact rates between individuals when movement is modelled by a correlated random walk

Bailey

2023

Theor Ecol

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Understanding how individuals come into contact with each other is important in many fields from biology and ecology to robotics and physics. Interaction dynamics are central in understanding how information is spread between agents, how disease spreads through a population, and how group movement or behaviour occurs. However, in many applications, the underlying mode of movement is not considered, and instead, contacts are considered a fraction of all possible contacts amongst a population. This gives rise to the mass-action law which in turn implies a negative quadratic relationship between contacts and individuals. Here we consider how a simple but often used movement model, the correlated random walk, affects the contact rate in a standard Susceptible-Infection (SI) epidemiological model. Via extensive simulation, we show that the contact rate is not always well described by the assumed negative quadratic relationship, $$I(N-I)$$ I ( N - I ) (where $$I$$ I is the number of infected at a given time and $$N$$ N the total number of individuals). Instead, we find that a contact rate proportional to $${\left[I(N-I)\right]}^{\alpha }$$ I ( N - I ) α with $$0<\alpha \le 1$$ 0 < α ≤ 1 is a better qualitative fit, where $$\alpha$$ α depends upon parameters such as the straightness of the movement and the density of individuals. We highlight that the expected contacts at low densities increase with straight line movement, whereas, at high densities, they increase with more random movement.

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Dynamics of interacting particle systems: Modeling implications of the repulsive interactions and experiments on magnetic prototypes

Cited by 6 publications

References 19 publications

Tunable band gaps and symmetry breaking in magnetomechanical metastructures inspired by multilayer two-dimensional materials

Tunable band gaps and symmetry breaking in magnetomechanical metastructures inspired by multilayer two-dimensional materials

Exploiting Localized Transition Waves to Tune Sound Propagation in Soft Materials

An assessment of the contact rates between individuals when movement is modelled by a correlated random walk

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