Structural heterogeneity: a topological characteristic to track the time evolution of soft matter systems

Ingrid Membrillo Solis; Tetiana Orlova; Karolina Bednarska; Piotr Lesiak; Tomasz R. Woliński; Giampaolo D'Alessandro; Jacek Brodzki; Malgosia Kaczmarek

arXiv · 2106.13169

Structural heterogeneity: a topological characteristic to track the time evolution of soft matter systems

Ingrid Membrillo Solis·Tetiana Orlova·Karolina Bednarska·Piotr Lesiak·Tomasz R. Woliński·Giampaolo D'Alessandro·Jacek Brodzki·Malgosia Kaczmarek

View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce structural heterogeneity, a new topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder transition at the microscopic scale. Such quantitative characterisation of a complex, soft matter system has not yet been achieved with any other method. We show that structural heterogeneity can track structural changes in a liquid crystal nanocomposite, reveal the effect of confined geometry on the nematic-isotropic and isotropic-nematic phase transitions, and uncover physical differences between these two processes. The system used in this work is representative of a class of composite nanomaterials, partially ordered and with complex structural and physical behaviour, where their precise characterisation poses significant challenges. Our newly developed analytic framework can provide both a qualitative and a quantitative characterisations of the dynamical behaviour of a wide range of semi-ordered soft matter systems.

Explore related subjects

cond-mat.soft math.AT physics.data-an physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Ingrid Membrillo Solis, Tetiana Orlova, Karolina Bednarska, Piotr Lesiak, Tomasz R. Woliński, Giampaolo D'Alessandro, Jacek Brodzki, Malgosia Kaczmarek. 2021-06-24. Structural heterogeneity: a topological characteristic to track the time evolution of soft matter systems. https://arxiv.org/abs/2106.13169

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↗