arXiv subjects

Karsten Kruse

Publications and source records attributed to Karsten Kruse.

At least 19 recordsLinked to original sources

arXiv2026

Strongly continuous and locally equicontinuous families of operators and their relation to bi-continuity

We study strongly continuous and locally equicontinuous families of operators on sequentially complete Hausdorff locally convex spaces. In case of Saks spaces, we relate the general notions to bi-continuity as well as equitightness. In this way, we recover and also generalise known results for special classes of operator families such as bi-continuous ($C$-)semigroups and ($C$-)cosine families by well-known results for the corresponding families in Hausdorff locally convex spaces.

math.FA↗

arXiv2026

Active topological strings in renewing nematopolar fluids

Active matter often simultaneously exhibits different kinds of orientational order and, in many cases of biological interest, undergoes continuous material renewal. In renewing nematopolar fluids we find stable topological strings, structures consisting of two nematic point defects connected by a defect line in the polar field. We identify the mechanism underlying string stabilization and unveil how string length is determined. In the presence of active stress, we observe active-string chaos. Our work identifies continuous material renewal as a generic mechanism underlying the stabilization of topological defect structures in systems with mixed order parameters. It could be used for orchestrating living matter during development and other biological processes.

cond-mat.soft↗

arXiv2025

Spatiotemporal Control of Charge +1 Topological Defects in Polar Active Matter

Topological defects are a conspicuous feature of active liquid crystals that have been associated with important morphogenetic transitions in organismal development. Robust development thus requires a tight control of the motion and placement of topological defects. In this manuscript, we study a mechanism to control +1 topological defects in an active polar fluid confined to a disk. If activity is localized in an annulus within the disk, the defect moves on a circular trajectory around the center of the disk. Using an ansatz for the polar field, we determine the dependence of the angular speed and the circle radius on the boundary orientation of the polar field and the active annulus. Using a proportional integral controller, we guide the defect along complex trajectories by changing the active annulus size and the boundary orientation.

cond-mat.soft↗

arXiv2025

Spectral theory for semigroups on locally convex spaces

In this paper we provide spectral inclusion and mapping theorems for strongly continuous locally equicontinuous semigroups on Hausdorff locally convex spaces. Our results extend the classical spectral inclusion and mapping theorems for strongly continuous semigroups on Banach spaces.

math.FA↗

arXiv2025

Defect states in compressible active polar fluids with turnover

Biological active matter like the cytoskeleton or tissues are characterized by their ability to transform chemical energy into mechanical stress. In addition, it often exhibits orientational order, which is essential for many cellular and morphogenetic processes. Experimental evidence suggests that defects in the orientational order field play an important role in organizing active stress. However, defects tend to annihilate unless the material is in a chaotic state or hydrodynamic interactions are suppressed. Using a hydrodynamic description of compressible active polar fluids, we show that turnover readily leads to a stabilization of defects. Depending on the turnover rate, topological defects arrange in a multitude of different phases, including lattices, active foams, and vortex glasses. Our work suggests that turnover plays a crucial role for organizing biological active matter.

physics.bio-ph↗

arXiv2025

The importance of being discrete -- An agent-based model for active nematics and more

We propose an agent-based model of active flexible rods. Inspired by cytoskeletal flows, we introduce activity by an internal flow that contributes to the dissipative forces. The active force between our agents is central and reciprocal, ensuring linear and angular momentum conservation. For nematic activity, we find spontaneous, thresholdless flows and stochastic flow-reorientation, which is accompanied by the formation of topological defects. Defects appear and vanish with activity-dependent rates, and $+1/2$-defects self-propel. These hallmarks of active turbulence are present even on the scale of individual agents. The particle-based interactions lead to an emergent coupling between density and orientation that generates density dipoles around $+1/2$-defects. Finally, we highlight the versatility of our agent-based model by presenting spontaneous flows in three dimensions and tissue growth. Our framework opens the way for an integrated description of living materials, including several forms of activity in the same system.

cond-mat.soft↗

arXiv2024

Noise-induced transitions from contractile to extensile active stress in isotropic fluids

Tissues of living cells are a prime example of active fluids. There is experimental evidence that tissues generate extensile active stress even though their constituting cells are contractile. Fluctuating forces that could result from cell-substrate interactions have been proposed to be able to induce a transition from contractile to extensile active stress. Through analytic calculations and numerical computations, we show that in isotropic active fluids, nonlinearities and a coupling between fluctuating forces and fluid density are necessary for such a transition to occur. Here, both transitions from extensile to contractile and vice versa are possible.

cond-mat.soft↗

arXiv2024

Continuous maximal regularity in locally convex spaces

We study maximal regularity with respect to continuous functions for strongly continuous semigroups on locally convex spaces as well as its relation to the notion of admissible operators. This extends several results for classical strongly continuous semigroups on Banach spaces. In particular, we show that Travis' characterization of $\mathrm{C}$-maximal regularity using the notion of bounded semivariation carries over to the general case. Under some topological assumptions, we further show the equivalence between maximal regularity and admissibility in this context.

math.FA↗

arXiv2024

Acto-myosin clusters as active units shaping living matter

Stress generation by the actin cytoskeleton shapes cells and tissues. Despite impressive progress in live imaging and quantitative physical descriptions of cytoskeletal network dynamics, the connection between processes at molecular scales and cell-scale spatio-temporal patterns is still unclear. Here we review studies reporting acto-myosin clusters of micrometer size and with lifetimes of several minutes in a large number of organisms ranging from fission yeast to humans. Such structures have also been found in reconstituted systems in vitro and in theoretical analysis of cytoskeletal dynamics. We propose that tracking these clusters can serve as a simple readout for characterising living matter. Spatio-temporal patterns of clusters could serve as determinants of morphogenetic processes that play similar roles in diverse organisms.

q-bio.TO↗

arXiv2024

Weighted composition semigroups on spaces of continuous functions and their subspaces

This paper is dedicated to weighted composition semigroups on spaces of continuous functions and their subspaces. We consider semigroups induced by semiflows and semicocycles on Banach spaces $\mathcal{F}(Ω)$ of continuous functions on a Hausdorff space $Ω$ such that the norm-topology is stronger than the compact-open topology like the Hardy spaces, the weighted Bergman spaces, the Dirichlet space, the Bloch type spaces, the space of bounded Dirichlet series and weighted spaces of continuous or holomorphic functions. It was shown by Gallardo-Gutiérrez, Siskakis and Yakubovich that there are no non-trivial norm-strongly continuous weighted composition semigroups on Banach spaces $\mathcal{F}(\mathbb{D})$ of holomorphic functions on the open unit disc $\mathbb{D}$ such that $H^{\infty}\subset\mathcal{F}(\mathbb{D})\subset\mathcal{B}_{1}$ where $H^{\infty}$ is the Hardy space of bounded holomorphic functions on $\mathbb{D}$ and $\mathcal{B}_{1}$ the Bloch space. However, we show that there are non-trivial weighted composition semigroups on such spaces which are strongly continuous w.r.t. the mixed topology between the norm-topology and the compact-open topology. We study such weighted composition semigroups in the general setting of Banach spaces of continuous functions and derive necessary and sufficient conditions on the spaces involved, the semiflows and semicocycles for strong continuity w.r.t. the mixed topology and as a byproduct for norm-strong continuity as well. Moreover, we give several characterisations of their generator and their space of norm-strong continuity.

math.FA↗

arXiv2024

Active self-disassembly enhances the yield of self-assembled structures

We introduce a lattice model to probe the effect of active self-disassembly on equilibrium self-assembly. Surprisingly, we find conditions under which active self-disassembly enhances the yield of a target structure above that achieved by self-assembly alone when the latter is already favoured thermodynamically. We discuss biological implications of our findings.

cond-mat.soft↗

arXiv2024

Sun dual theory for bi-continuous semigroups

The sun dual space corresponding to a strongly continuous semigroup is a known concept when dealing with dual semigroups, which are in general only weak$^*$-continuous. In this paper we develop a corresponding theory for bi-continuous semigroups under mild assumptions on the involved locally convex topologies. We also discuss sun reflexivity and Favard spaces in this context, extending classical results by van Neerven.

math.FA↗

arXiv2024

On linearisation and existence of preduals

We study the problem of existence of preduals of locally convex Hausdorff spaces. We derive necessary and sufficient conditions for the existence of a predual with certain properties of a bornological locally convex Hausdorff space $X$. Then we turn to the case that $X=\mathcal{F}(Ω)$ is a space of scalar-valued functions on a non-empty set $Ω$ and characterise those among them which admit a special predual, namely a strong linearisation, i.e. there are a locally convex Hausdorff space $Y$, a map $δ\colonΩ\to Y$ and a topological isomorphism $T\colon\mathcal{F}(Ω)\to Y_{b}'$ such that $T(f)\circ δ= f$ for all $f\in\mathcal{F}(Ω)$.

math.FA↗

arXiv2024

Mixed topologies on Saks spaces of vector-valued functions

We study Saks spaces of functions with values in a normed space and the associated mixed topologies. We are interested in properties of such Saks spaces and mixed topologies which are relevant for applications in the theory of bi-continuous semigroups. In particular, we are interested if such Saks spaces are complete, semi-Montel, C-sequential or a (strong) Mackey space with respect to the mixed topology. Further, we consider the question whether the mixed and the submixed topology coincide on such Saks spaces and seek for explicit systems of seminorms that generate the mixed topology.

math.FA↗

arXiv2023

Localized spatiotemporal dynamics in active fluids

From cytoskeletal networks to tissues, many biological systems behave as active materials. Their composition and stress-generation is affected by chemical reaction networks. In such systems, the coupling between mechanics and chemistry enables self-organization, for example, into waves. Recently, contractile mechanochemical systems were shown to be able to spontaneously develop localized spatial patterns. Here, we show that these localized patterns can present intrinsic spatiotemporal dynamics, including oscillations and chaotic-like dynamics. We discuss their physical origin and bifurcation structure.

physics.bio-ph↗

arXiv2023

Localized states in active fluids

Biological active matter is typically tightly coupled to chemical reaction networks affecting its assembly-disassembly dynamics and stress generation. We show that localized states can emerge spontaneously if assembly of active matter is regulated by chemical species that are advected with flows resulting from gradients in the active stress. The mechanochemical localized patterns form via a subcritical bifurcation and for parameter values for which patterns do not exist in absence of the advective coupling. Our work identifies a generic mechanism underlying localized cellular patterns.

physics.bio-ph↗

arXiv2023

On linearisation, existence and uniqueness of preduals: The isometric case

We study the problem of existence and uniqueness of isometric Banach preduals of a Banach space. We derive necessary and sufficient conditions for the existence of an isometric Banach predual of a Banach space $X$. Then we focus on the case that $X=\mathcal{F}(\Omega)$ is a Banach space of scalar-valued functions on a non-empty set $\Omega$ and describe those spaces which admit a special isometric Banach predual, namely a \emph{strong isometric Banach linearisation}, i.e. there is a Banach space $Y$, a map $\delta\colon\Omega\to Y$ and an isometric isomorphism $T\colon\mathcal{F}(\Omega)\to Y^{\ast}$ such that $T(f)\circ \delta= f$ for all $f\in\mathcal{F}(\Omega)$. Finally, we give necessary and sufficient conditions for Banach spaces $\mathcal{F}(\Omega)$ with a strong isometric Banach linearisation to have a (strongly) unique isometric Banach predual.

math.FA↗

arXiv2023

Density-polarity coupling in confined active polar films: asters, spirals, and biphasic orientational phases

Topological defects in active polar fluids can organise spontaneous flows and influence macroscopic density patterns. Both of them play, for example, an important role during animal development. Yet the influence of density on active flows is poorly understood. Motivated by experiments on cell monolayers confined to discs, we study the coupling between density and polar order for a compressible active polar fluid in presence of a +1 topological defect. As in the experiments, we find a density-controlled spiral-to-aster transition. In addition, biphasic orientational phases emerge as a generic outcome of such coupling. Our results highlight the importance of density gradients as a potential mechanism for controlling flow and orientational patterns in biological systems.

cond-mat.soft↗