arXiv subjects

Naomi Oppenheimer

Publications and source records attributed to Naomi Oppenheimer.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical Spreading and Memory Retention Under Power Law Potential

We study the overdamped dynamic spreading of a suspension of particles under a repulsive power law potential. We predict that the suspension spreads in a self-similar form, with its radius growing in time with a power independent of the dimension. We confirm this prediction experimentally using magnetized colloids with dipolar repulsion. Numerical simulations corroborate the experiments and further predict a categorically different behavior at a critical power, below which the initial distribution is no longer concentrated at the origin. Instead, particles accumulate at the perimeter and retain a long-lived memory of their original pattern. Below this threshold, the initial distribution seeds the resulting pattern, encoding the future structure of a dynamically evolving system.

cond-mat.soft↗

arXiv2025

Shape transitions of sedimenting confined droplets and capsules: from oblate to bullet-like geometries

The transport and deformation of confined droplets and flexible capsules are central to diverse phenomena and applications, from biological flows in microcapillaries to industrial processes in porous media. Inspired by experiments, we perform numerical simulations to investigate their shape dynamics under varying levels of confinement and particle flexibility. A transition from an oblate to a bullet-like shape is observed at a confinement threshold, independent of flexibility, which agrees with our analytical calculations. A fluid-structure interaction analysis reveals two regimes: a pressure-dominated and a viscous-dominated regime. For highly flexible particles, the pressure-dominated regime prevails and the deformation is enhanced. These findings offer new insights into the transport of flexible particles in confined environments, with implications for biomedical applications, filtration technologies, and multiphase fluid mechanics.

cond-mat.soft↗

arXiv2025

A geometric condition for robot-swarm cohesion and cluster-flock transition

We present a geometric design rule for size-controlled clustering of self-propelled particles. We show that active particles that tend to rotate under an external force have an intrinsic, signed parameter with units of curvature which we call curvity, that can be derived from first principles. Experiments with robots and numerical simulations show that properties of individual robots (radius and curvity) control pair cohesion in a binary system, and the stability of flocking and self-limiting clustering in a swarm, with applications in meta-materials and in embodied decentralized control.

cond-mat.soft↗

arXiv2025

Enhancement and Suppression of Active Particle Movement Due to Membrane Deformations

Microswimmers and active colloids often move in confined systems, including those involving interfaces. Such interfaces, especially at the microscale, may deform in response to the stresses of the flow created by the active particle. We develop a theoretical framework to analyze the effect of a nearby membrane due to the motion of an active particle whose flow fields are generated by force-free singularities. We demonstrate our result on a particle represented by a combination of a force dipole and a source dipole, while the membrane resists deformation due to tension and bending rigidity. We find that the deformation either enhances or suppresses the motion of the active particle, depending on its orientation and the relative strengths between the fundamental singularities that describe its flow. Furthermore, the deformation can generate motion in new directions.

cond-mat.soft↗

arXiv2025

Dynamical Spreading Under Power Law Potential

We examine the dynamic spreading of a dense overdamped suspension of particles under power law repulsive potentials, often called Riesz gases. That is, potentials that decay with distance as 1/r^k where k\in (-2,\infty]. Depending on the value of k relative to the system's spatial dimension $D$, the potentials are categorized as short-ranged for k > D, and long-ranged when $k \leq D$. Such systems naturally occur in contexts involving particle suspensions, granular media, and charged systems, where interactions can be influenced by physical fields that decrease over distance. Our analytical findings reveal that the particles spread in a self-similar form, with the radius growing with time as t^1/(k+2). The theoretical predictions derived for a general dimension D, are verified by numerical simulations involving thousands of particles in free space, in both one and two dimensions. Furthermore, the simulations not only confirm our analytical results but also reveal a rich diversity of behaviors depending on the value of k. We demonstrate that the density profiles differ significantly depending on whether k is larger than, smaller than, or equal to D-2, where D is the dimension. For k>D-2 the density is centered in the middle and we also notice a Wigner lattice emerging as a result of the repulsive interactions, for k = D-2, density is uniform and for k<D-2, density is centered at the edges. This new classification indicates that the long/short-range classification is insufficient for predicting the density profile of the suspension. When k<D-2, we observed an interesting phenomenon when two or more suspensions are placed near each other: a particle-free zone is formed where the two populations meet, resembling structures of bubbles.

cond-mat.soft↗

arXiv2024

Hydrodynamics of molecular rotors in lipid membranes

Molecular rotors form twisted conformations upon photoexcitation, with their fluorescent relaxation time serving as a measure of viscosity. They have been used to assess membrane viscosities but yield higher values compared to other methods. Here, we show that the rotor's relaxation time is influenced by a combination of membrane viscosity and interleaflet friction. We present a theory for the relaxation time and obtain a correction factor that accounts for the discrepancy. If the membrane's viscosity is known, molecular rotors may enable the extraction of the elusive interleaflet friction.

cond-mat.soft↗

arXiv2024

A Mechanical Route for Cooperative Transport in Autonomous Robotic Swarms

Cooperative transport is a striking phenomenon where multiple agents join forces to transit a payload too heavy for the individual. While social animals such as ants are routinely observed to coordinate transport at scale, reproducing the effect in artificial swarms remains challenging, as it requires synchronization in a noisy many-body system. Here we show that cooperative transport spontaneously emerges in swarms of stochastic self-propelled robots. Robots deprived of sensing and communication, are isotropically initialized around a passive circular payload, where directional motion is not expected without an external cue. And yet it moves. We find that a minute modification to the mechanical design of the individual agent dramatically changes its alignment response to an external force. We then show experimentally that by controlling the individual's friction and mass distribution, a swarm of active particles autonomously cooperates in the directional transport of larger objects. Surprisingly, transport increases with increasing payload size, and its persistence surpasses the persistence of the active particles by over an order of magnitude. A mechanical, coarse-grained description reveals that force-alignment is intrinsic and captured by a signed, charge-like parameter with units of curvature. Numerical simulations of swarms of active particles with a negative active charge corroborate the experimental findings. We analytically derive a geometrical criterion for cooperative transport which results from a bifurcation in a non-linear dynamical system. Our findings generalize existing models of active particles, offer new design rules for distributed robotic systems, and shed light on cooperation in natural swarms.

cond-mat.soft↗

arXiv2024

Hydrodynamic Spin-Pairing and Active Polymerization of Oppositely Spinning Rotors

Rotors are common in nature - from rotating membrane-proteins to superfluid-vortices. Yet, little is known about the collective dynamics of heterogeneous populations of rotors. Here, we show experimentally, numerically, and analytically that at small but finite inertia, a mixed population of oppositely spinning rotors spontaneously self-assembles into active chains, which we term gyromers. The gyromers are formed and stabilized by fluid motion and steric interactions alone. A detailed analysis of pair interaction shows that rotors with the same spin repel and orbit each other while opposite rotors spin-pair and propagate together as bound dimers. Rotor dimers interact with individual rotors, each other, and the boundaries to form chains. A minimal model predicts the formation of gyromers in numerical simulations and their possible subsequent folding into secondary structures of lattices and rings. This inherently out-of-equilibrium polymerization process holds promise for engineering self-assembled metamaterials such as artificial proteins.

cond-mat.soft↗

arXiv2024

Effective Viscosity of a Suspension of Hot Particles

Active particles with a temperature distribution, "hot particles", have a distinct effect on the fluid that surrounds them. The temperature gradients they create deem the fluid's viscosity spatially dependent, therefore violating the linearity of the problem, making a full description of velocity and pressure fields challenging. Using energy dissipation analysis and Lorentz Reciprocal Theorem, we show that it is still possible to study global properties of such hot suspensions. Namely, we calculate the effective viscosity of a dilute hot suspension, adding a correction that includes contributions from the bulk fluid and the particles themselves. As examples of this method, we derive the effective viscosity of a suspension of spherical particles with different heat distributions. We show that when the particles are non-Brownian and are all oriented in the same direction, the viscosity is no longer isotropic and depends on the direction of the shear relative to the orientation of the particles. If the particles' orientation is fixed due to an external field, the stress tensor is no longer symmetric, and the viscosity has odd components.

cond-mat.soft↗

arXiv2024

Compact expansion of a repulsive suspension

Short-range repulsion governs the dynamics of matter from atoms to animals. Using theory, simulations, and experiments, we find that an ensemble of repulsive particles spreads compactly with a sharp boundary, in contrast to the diffusive spreading of Brownian particles. Starting from the pair interactions, at high densities, the many-body dynamics follow non-linear diffusion with a self-similar expansion, growing as $t^{1/4}$; At longer times, thermal motion dominates with the classic $t^{1/2}$ expansion. A logarithmic growth controlled by nearest-neighbor interactions connects the two self-similar regimes.

cond-mat.soft↗

arXiv2023

Hydrodynamically Induced Aggregation in Two-Dimensional Active Systems

We investigate a system of co-oriented active particles interacting only via hydrodynamic and steric interactions. We offer a new method of calculating the flow created by any active particle in a 2D fluid, focusing on the dynamics of flow fields with a high-order spatial decay, which we analyze using a geometric Hamiltonian. We show that when orientational degrees of freedom are quenched, and the flow has a single, odd power decay, such many-particle systems lead to stable, fractal-like aggregation, with the only exceptions being the force dipole. We discuss how our results can easily be generalized to more complicated force distributions and to other effective two-dimensional systems.

cond-mat.soft↗

arXiv2023

Hamiltonian Dynamics and Structural States of Two-Dimensional Microswimmers

We show that a two-dimensional system of flocking microswimmers interacting hydrodynamically can be expressed using a Hamiltonian formalism. The Hamiltonian depends strictly on the angles between the particles and their swimming orientation, thereby restricting their available phase-space. Simulations of co-oriented microswimmers evolve into "escalators" - sharp lines at a particular tilt along which particles circulate. The conservation of the Hamiltonian and its symmetry germinate the self-assembly of the observed steady-state arrangements as confirmed by stability analysis.

cond-mat.soft↗

arXiv2021

Vortex Flows and Streamline Topology in Curved Biological Membranes

When considering flows in biological membranes, they are usually treated as flat, though more often than not, they are curved surfaces, even extremely curved, as in the case of the endoplasmic reticulum. Here, we study the topological effects of curvature on flows in membranes. Focusing on a system of many point vortical defects, we are able to cast the viscous dynamics of the defects in terms of a geometric Hamiltonian. In contrast to the planar situation, the flows generate additional defects of positive index. For the simpler situation of two vortices, we analytically predict the location of these stagnation points. At the low curvature limit, the dynamics resemble that of vortices in an ideal fluid, but considerable deviations occur at high curvatures. The geometric formulation allows us to construct the spatio-temporal evolution of streamline topology of the flows resulting from hydrodynamic interactions between the vortices. The streamlines reveal novel dynamical bifurcations leading to spontaneous defect-pair creation and fusion. Further, we find that membrane curvature mediates defect binding and imparts a global rotation to the many-vortex system, with the individual vortices still interacting locally.

physics.flu-dyn↗

arXiv2021

Hyperuniformity and phase enrichment in vortex and rotor assemblies

Ensembles of particles rotating in a two-dimensional fluid can exhibit chaotic dynamics yet develop signatures of hidden order. Such "rotors" are found in the natural world spanning vastly disparate length scales - from the rotor proteins in cellular membranes to models of atmospheric dynamics. Here we show that an initially random distribution of either ideal vortices in an inviscid fluid, or driven rotors in a viscous membrane, spontaneously self assembles. Despite arising from drastically different physics, these systems share a Hamiltonian structure that sets geometrical conservation laws resulting in distinct structural states. We find that the rotationally invariant interactions isotropically suppress long wavelength fluctuations - a hallmark of a disordered hyperuniform material. With increasing area fraction, the system orders into a hexagonal lattice. In mixtures of two co-rotating populations, the stronger population will gain order from the other and both will become phase enriched. Finally, we show that classical 2D point vortex systems arise as exact limits of the experimentally accessible microscopic membrane rotors, yielding a new system through which to study topological defects.

cond-mat.soft↗

arXiv2019

Fast crystallization of rotating membrane proteins

We examine the interactions between actively rotating proteins moving in a membrane. Experimental evidence suggests that such rotor proteins, like the ATP synthases of the inner mitochondrial membrane, can arrange themselves into lattices. We show that crystallization is possible through a combination of hydrodynamic and repulsive interactions between the rotor proteins. In particular, hydrodynamic interactions induce rotational motion of the rotor protein assembly that, in the presence of repulsion, drives the system into a hexagonal lattice. The entire crystal rotates with an angular velocity which increases with motor density and decreases with lattice diameter - larger and sparser arrays rotate at a slower pace. The rotational interactions allow ensembles of proteins to sample configurations and reach an ordered steady state, which are inaccessible to the quenched nonrotational system. Rotational interactions thus act as a sort of temperature that removes disorder, except that actual thermal diffusion leads to expansion and loss of order. In contrast, the rotational interactions are bounded in space. Hence, once an ordered state is reached, it is maintained at all times.

cond-mat.soft↗

arXiv2018

Surfing its own wave: hydroelasticity of a particle near a membrane

We show using theory and experiments that a small particle moving along an elastic membrane through a viscous fluid is repelled from the membrane due to hydro-elastic forces. The viscous stress field produces an elastic disturbance leading to particle-wave coupling. We derive an analytic expression for the particle trajectory in the lubrication limit, bypassing the construction of the detailed velocity and pressure fields. The normal force is quadratic in the parallel speed, and is a function of the tension and bending resistance of the membrane. Experimentally, we measure the normal displacement of spheres sedimenting along an elastic membrane and find quantitative agreement with the theoretical predictions with no fitting parameters. We experimentally demonstrate the effect to be strong enough for particle separation and sorting. We discuss the significance of these results for bio-membranes and propose our model for membrane elasticity measurements.

cond-mat.soft↗

arXiv2015

A shapeable material without plastic deformation

Randomly crumpled sheets have shape memory. In order to understand the basis of this form of memory, we simulate triangular lattices of springs whose lengths are altered to create a topography with multiple potential energy minima. We then deform these lattices into different shapes and investigate their ability to retain the imposed shape when the energy is relaxed. The lattices are able to retain a range of curvatures. Under moderate forcing from a state of local equilibrium, the lattices deform by several percent but return to their retained shape when the forces are removed. By increasing the forcing until an irreversible motion occurs, we find that the transitions between remembered shapes show co-operativity among several springs. For fixed lattice structures, the shape memory tends to decrease as the lattice is enlarged; we propose ways to counter this decrease by modifying the lattice geometry. We survey the energy landscape by displacing individual nodes. An extensive fraction of these nodes proves to be bistable; they retain their displaced position when the energy is relaxed. Bending the lattice to a stable curved state alters the pattern of bistable nodes. We discuss this shapeability in the context of other forms of material memory and contrast it with the shapeability of plastic deformation. We outline the prospects for making real materials based on these principles.

cond-mat.soft↗

arXiv2013

Anomalously fast kinetics of lipid monolayer buckling

We re-examine previous observations of folding kinetics of compressed lipid monolayers in light of the accepted mechanical buckling mechanism recently proposed [L. Pocivavsek et al., Soft Matter, 2008, 4, 2019]. Using simple models, we set conservative limits on a) the energy released in the mechanical buckling process and b) the kinetic energy entailed by the observed folding motion. These limits imply a kinetic energy at least thirty times greater than the energy supplied by the buckling instability. We discuss possible extensions of the accepted picture that might resolve this discrepancy.

cond-mat.soft↗