Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1006.3569

Correlated dynamics of inclusions in a supported membrane

Naomi Oppenheimer·Haim Diamant
View original source ↗Read source document ↗Export metadata ↓

Abstract

The hydrodynamic theory of heterogeneous fluid membranes is extended to the case of a membrane adjacent to a solid substrate. We derive the coupling diffusion coefficients of pairs of membrane inclusions in the limit of large separation compared to the inclusion size. Two-dimensional compressive stresses in the membrane make the coupling coefficients decay asymptotically as $1/r^2$ with interparticle distance $r$. For the common case, where the distance to the substrate is of sub-micron scale, we present expressions for the coupling between distant disklike inclusions, which are valid for arbitrary inclusion size. We calculate the effect of inclusions on the response of the membrane and the associated corrections to the coupling diffusion coefficients to leading order in the concentration of inclusions. While at short distances the response is modified as if the membrane were a two-dimensional suspension, the large-distance response is not renormalized by the inclusions.

Explore related subjects

cond-mat.softphysics.bio-phphysics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Naomi Oppenheimer, Haim Diamant. 2010-11-09. Correlated dynamics of inclusions in a supported membrane. https://doi.org/10.1103/physreve.82.041912

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Spontaneous Vortex Instability in Active Nematics

One of the defining results in the study of active matter is the spontaneous flow instability, through which a homogeneous, uniformly aligned state breaks translational symmetry along a single direction and develops sustained flow. The vortex state that emerges at higher activity has instead been attributed to nonlinear dynamics. Using a Floquet-type linear stability analysis, we show that no such mechanism is required: the flowing state undergoes a secondary, zigzag instability that breaks the remaining translational symmetry and produces the vortex state. We further identify a regime in which the flowing state ceases to exist and vortices emerge directly from the uniformly aligned state. Under channel confinement, the instability selects a length scale that differs from the establishedactivelengthscale, andsetsthenumberofvorticesthatappear, leadingtoaconfinement- selected pattern reminiscent of a vortex lattice, opening a route toward direct experimental tests of this instability. Full nonlinear simulations reproduce the predicted onset activities and the selected vortex number.

cond-mat.soft↗
arXiv2026

Active pistons extract work by periodic compression alone

Active matter is liable to invent protocols that evade the constraints of equilibrium thermodynamics. We put forward active pistons that extract work by periodic compression alone without changing any bulk property of the system. Such pistons necessarily couple the perturbation imposed by an external operator with some degrees of freedom internal to active components. We illustrate this design principle with elastic networks composed of self-aligning motile particles. For slow protocols, self-alignment always overwhelms mechanical friction when the internal activity exceeds a specific threshold controlled by fluctuations. We identify the key response coefficient that helps delineate regimes of work extraction, and reveal that the corresponding phase diagram follows a master curve with re-entrance in terms of noise amplitude. Overall, our active pistons embody a novel design principle with broad implications for building innovative engines far from equilibrium.

cond-mat.soft↗
arXiv2026

Geometry-induced flocking and topological sound on a defect-free curved surface

We study an ordered polar active flock on a torus and show that topological sound persists on a compact curved surface without topological defects or physical boundaries. Using the covariant Toner Tu theory, we derive an effective nonHermitian Dirac operator whose curvature-induced mass changes sign across the outer and inner equators, producing two Jackiw Rebbi domain walls. These support co-propagating but distinct chiral edge excitations: a density mode localized on the positively curved outer equator and a Goldstone mode localized on the negatively curved inner equator. The bulk bands possess opposite half-integer Chern numbers whose jumps across the domain walls are determined by the sign of the Gaussian curvature. We further show that the localised modes are protected by a one-dimensional Callias index theorem, while the sum of the local indices obeys the Poincare Hopf theorem on the compact surface. Our results establish that curvature alone, independent of defects and boundaries, is sufficient to generate and protect topological sound in active matter, providing a unified connection between non-Hermitian topology, differential geometry, and hydrodynamic theory of collective motion.

cond-mat.soft↗