arXiv subjects

Andreas M. Menzel

Publications and source records attributed to Andreas M. Menzel.

At least 19 recordsLinked to original sources

arXiv2026

Brownian yet non-Gaussian diffusion through equilibrium nonlinear friction

In Brownian yet non-Gaussian diffusion (BnGD) the mean squared displacement grows linearly in time. However, the displacement statistics do not follow a normal distribution throughout. Typically, they are non-Gaussian at intermediate times, before they cross over to Gaussian in the long-time regime. We demonstrate that nonlinear friction under correctly applied stochastic equilibrium conditions provides an explanation of this phenomenon also for homogeneous environments.

cond-mat.stat-mech↗

arXiv2026

Hydrodynamic flows induced by localized torques (rotlets) in wedge-shaped geometries

Wedge-shaped geometries in low-Reynolds-number flows are of increasing importance, for instance, in the design of microfluidic devices. The corresponding Green's functions describing the induced flow in response to a locally applied force were derived some time ago. To achieve a complete characterization of particle motion at low Reynolds numbers, we derive the flow response to locally applied torques. This is accomplished through a direct calculation based on the Fourier-Kontorovich-Lebedev transform using the Papkovich-Neuber representation of the hydrodynamic fields. We then illustrate the resulting flow fields, highlighting their structure, key features, and dependence on the geometry and orientation of the applied torque. Based on these solutions, we compute the corresponding hydrodynamic mobility tensor that couples torque and motion. Owing to the broken spatial symmetry imposed by the wedge-shaped confinement, a particle subjected to a torque will experience not only rotational motion but also translational motion. These results provide analytical tools relevant for predicting and controlling particle behavior in confined microfluidic environments.

physics.flu-dyn↗

arXiv2026

Hydrodynamics substantially affects induced structure formation in magnetic fluids

Magnetorheological fluids consist of micrometer-sized magnetic particles in a carrier liquid. Sufficiently strong external magnetic fields lead to the formation of string-like particle aggregates. We demonstrate that hydrodynamic interactions, that is, mutual couplings via induced flows, play a substantial role during the structuring process. They support the formation of slender chains instead of more compact clusters in the absence of mutual hydrodynamic interactions between the particles. This fundamental insight is substantial from an application perspective, due to the enormous technical importance and potential of structured magnetorheological materials.

cond-mat.soft↗

arXiv2026

Magnetically Driven Elastic Microswimmers: Exploiting Hysteretic Collapse for Autonomous Propulsion and Independent Control

When swimming at low Reynolds numbers, inertial effects are negligible and reciprocal movements cannot induce net motion. Instead, symmetry breaking is necessary to achieve net propulsion. Directed swimming can be supported by magnetic fields, which simultaneously provide a versatile means of remote actuation. Thus, we analyze the motion of a straight microswimmer composed of three magnetizable beads connected by two elastic links. The swimming mechanism is based on oriented external magnetic fields that oscillate in magnitude. Through induced reversible hysteretic collapse of the two segments of the swimmer, the two pairs of beads jump into contact and separate nonreciprocally. Due to higher-order hydrodynamic interactions, net displacement results after each cycle. Different microswimmers can be tuned to different driving amplitudes and frequencies, allowing for simultaneous independent control by just one external magnetic field. The swimmer geometry and magnetic field shape are optimized for maximum swimming speed using an evolutionary optimization strategy. Thanks to the simple working principle, an experimental realization of such a microrobot seems feasible and may open new approaches for microinvasive medical interventions such as targeted drug delivery.

cond-mat.soft↗

arXiv2025

Diffusion through complex confining environments: fluctuating triply periodic minimal surfaces

The transport of individual entities through interconnected structures is a process of practical relevance both in biology and technology. Examples are given by diffusive dynamics of molecules in porous structures. In soft environments, this transport can be strongly influenced by fluctuations of the porous structure itself. Here, we focus on triply periodic membrane structures found both in cell organelles and in synthetic amphiphilic systems. We theoretically study the effect of a complex three-dimensional fluctuating environment on the diffusive motion of a test object, using a phase field approach. The rigid spherical test object is energetically forced to not penetrate the membrane. Generally, the pores of the membrane structure can be smaller than the diffusing object. Yet, fluctuations of the membrane can intermittently widen its pores, still allowing for the motion of the larger particles through them. Thus, the object stays trapped for a while inside one cavity formed by the membrane, before an appropriate fluctuation event widens a membrane pore in the right moment so that the object can jump into the next cavity. The process is reflected by a pronounced plateau in the time evolution of the mean squared displacement. We think that the described scenario should be directly observable, for instance, in protein diffusion through biological environments.

cond-mat.soft↗

arXiv2025

Mechanically concealed holes

When a hole is introduced into an elastic material, it will usually act to reduce the overall mechanical stiffness. A general ambition is to investigate whether a stiff shell around the hole can act to maintain the overall mechanical properties. We consider this effect from a macroscopic continuum perspective down to atomistic scales. For this purpose, we focus on the basic continuum example situation of an isotropic, homogeneous, linearly elastic material loaded uniformly under compressive plane strain for low concentrations of holes. As we demonstrate, the thickness of the shell can be adjusted in a way to maintain the overall stiffness of the system. We derive a corresponding mathematical expression for the thickness of the shell that conceals the hole. Thus, one can work with given materials to mask the presence of the holes simply by adjusting the thickness of the surrounding shells, with no need to change the materials. Our predictions from linear elasticity continuum theory are extended to atomistic levels using molecular dynamics simulations of a model Lennard-Jones solid. These extensions attest the robustness of our predictions down to atomistic scales. Thus, they open a straightforward possibility to adjust the strategy of mechanical cloaking via atomistic manipulations. From both perspectives, the underlying concept is important in the context of light-weight construction.

physics.class-ph↗

arXiv2025

Elastic displacements and viscous hydrodynamic flows in wedge-shaped geometries with a straight edge: Green's functions for parallel forces

For homogeneous and isotropic linearly elastic solids and for incompressible fluids under low-Reynolds-number conditions the fundamental solutions of the associated continuum equations were derived a long time ago for bulk systems. That is, the corresponding Green's functions are available in infinitely extended systems, where boundaries do not play any role. However, introducing boundaries renders the situation significantly more complex. Here, we derive the corresponding Green's functions for a linearly elastic homogeneous and isotropic material in a wedge-shaped geometry. Two flat boundaries confine the material and meet at a straight edge. No-slip and free-slip conditions are considered. The force is oriented in a direction parallel to the straight edge of the wedge. Assuming incompressibility, our expressions also apply to the situation of low-Reynolds-number hydrodynamic viscous fluid flows. Thus, they may be used, for instance, to describe the motion of self-propelled objects guided by an edge or the distortion of soft elastic actuators in wedge-shaped environments of operation.

cond-mat.soft↗

arXiv2025

Doubling the magnetorheological effect of magnetic elastomers

One of the most important properties of soft functionalized magnetic composite materials in view of their technological potential is given by the magnetorheological effect. It describes the change in rheological properties such as the shear modulus by application of external magnetic fields. We demonstrate how computational material design can support in approximately doubling the magnitude of this important phenomenon for magnetic elastomers. Key is to work with two perpendicular magnetic field directions. We expect future practical relevance of our concept.

cond-mat.soft↗

arXiv2025

Unified description of viscous, viscoelastic, or elastic thin active films on substrates

It is frequent for active or living entities to find themselves embedded in a surrounding medium. Resulting composite systems are usually classified as either active fluids or active solids. Yet, in reality, particularly in the biological context, a broad spectrum of viscoelasticity exists in between these two limits. There, both viscous and elastic properties are combined. To bridge the gap between active fluids and active solids, we here systematically derive a unified continuum-theoretical framework. It covers viscous, viscoelastic, and elastic active materials. Our continuum equations are obtained by coarse-graining a discrete, agent-based microscopic dynamic description. In our subsequent analysis, we mainly focus on thin active films on supporting substrates. Strength of activity and degree of elasticity are used as control parameters that control the overall behavior. We concentrate on the analysis of transitions between spatially uniform analytical solutions of collective migration. These include isotropic and polar, orientationally ordered states. A stationary polar solution of persistent directed collective motion is observed for rather fluid-like systems. It corresponds to the ubiquitous swarming state observed in various kinds of dry and wet active matter. With increasing elasticity, persistent motion in one direction is prevented by elastic anchoring and restoring forces. As a consequence, rotations of the spatially uniform migration direction and associated flow occur. Our unified description allows to continuously tune the material behavior from viscous, via viscoelastic, to elastic active behavior by variation of a single parameter. Therefore, it allows in the future to investigate the time evolution of complex systems and biomaterials such as biofilms within one framework.

cond-mat.soft↗

arXiv2025

Rheologically tuned modes of collective transport in active viscoelastic films

While many living biological media combine both viscous and elastic properties, most theoretical studies employ either purely fluid- or solid-like descriptions. We here use a unified framework for active films on substrates capable of describing a broad range of viscoelastic behavior to explore the interplay between activity and rheology. The core of the study is a comprehensive state diagram showing a rich world of spatiotemporal dynamic states. Our results demonstrate the potential of tunable rheology to realize modes of controlled active transport on the microscale.

cond-mat.soft↗

arXiv2025

Self-sustained patchy turbulence in shear-thinning active fluids

Bacterial suspensions and other active fluids are known to develop highly dynamical vortex states, denoted as active or mesoscale turbulence. We reveal the pronounced effect of non-Newtonian rheological conditions on these turbulent states, concentrating on shear thinning. A self-sustained heterogeneous state of coexisting turbulent and quiescent areas develops, which results in anomalous velocity statistics. The heterogeneous state emerges in a hysteretic transition when varying activity. We provide an extensive numerical analysis and observe features consistent with a directed percolation transition. Our results are important, for instance, when addressing active objects in biological media with complex rheological properties.

cond-mat.soft↗

arXiv2025

Elastic displacements and viscous flows in wedge-shaped geometries with a straight edge: Green's functions for perpendicular forces

Edges are abundant when elastic solids glide in guiding rails or fluids are contained in vessels. We here address induced displacements in elastic solids or small-scale flows in viscous fluids in the vicinity of one such edge. For this purpose, we solve the governing elasticity equations for linearly elastic, potentially compressible solids, as well as the low-Reynolds-number flow equations for incompressible fluids. Technically speaking, we derive the associated Green's functions under confinement by two planar boundaries that meet at a straight edge. The two boundaries both feature no-slip or free-slip conditions, or one of these two conditions per boundary. Previously, we solved the simpler case of the force being oriented parallel to the straight edge. Here, we complement this solution by the more challenging case of the force pointing into a direction perpendicular to the edge. Together, these two cases provide the general solution. Specific situations in which our analysis may find application in terms of quantitative theoretical descriptions are particle motion in confined colloidal suspensions, dynamics of active microswimmers near edges, or actuated distortions of elastic materials due to activated contained functionalized particles.

cond-mat.soft↗

arXiv2025

Effects of curvature on growing films of microorganisms

To provide insight into the basic properties of emerging structures when bacteria or other microorganisms conquer surfaces, it is crucial to analyze their growth behavior during the formation of thin films. In this regard, many theoretical studies focus on the behavior of elongating straight objects. They repel each other through volume exclusion and divide into two halves when reaching a certain threshold length. However, in reality, hardly any object of a certain elongation is perfectly straight. Therefore, we here study the consequences of the curvature of individuals on the growth of colonies and thin active films. This individual curvature, so far hardly considered, turns out to qualitatively affect the overall growth behavior of the colony. Particularly, strings of stacked curved cells emerge that show branched structures, while the size of orientationally ordered domains in the colony is significantly decreased. Furthermore, we identify emergent spatio-orientational coupling that is not observed in colonies of straight cells. Our results are important for a fundamental understanding of the interaction and spreading of microorganisms on surfaces, with implications for medical applications and bioengineering.

cond-mat.soft↗

arXiv2025

Linear theory of viscoelasticity in a generalized hydrodynamic framework

A generalized hydrodynamic theory that systematically incorporates elasticity and viscoelasticity had been derived about a quarter of a century ago. It is based on a strictly Euler point of view, as is natural for hydrodynamics. We used and adapted this theory particularly in a linear framework. There, it is straightforward to focus on what are the flow and displacement fields in linearized hydrodynamics and elasticity, which provides some advantages. Since this theoretical approach appears not to be as commonly widespread as it deserves to be, we here overview and review the formalism. Specific further focus is on pointing out relations to the commonly known Kelvin-Voigt model and Maxwell model. They are naturally contained within this description. The two limits of perfect long-term elasticity on one hand and long-term flow on the other hand can be represented by adjusting only one parameter.

physics.class-ph↗

arXiv2025

Oscillatory collective motion in viscoelastic and elastic active fluids and solids under circular confinement

In an inspiring recent study, Xu et al. [Nat. Phys. 19, 46 (2023)] observed for a living active biofilm under circular confinement two emergent dynamic modes of collective motion in the film. One corresponds to global rotational motion of oscillating sense of rotation, the other one to uniformly translating motion of rotating migration direction. The authors reproduced these features in a discretized theoretical model for elastic active solids. We here demonstrate that the discovered fundamental phenomena are generic and emerge abundantly for a broad range of viscoelastic fluids and solids. Elastic solids represent only one limiting case.

cond-mat.soft↗

arXiv2024

Collective excitations in active solids featuring alignment interactions

With increasing emphasis on the study of active solids, the features of these classes of nonequilibrium systems and materials beyond their mere existence shift into focus. One concept of active solids addresses them as active, self-propelled units that are elastically linked to each other. The emergence of orientationally ordered, collectively moving states in such systems has been demonstrated. We here analyze the excitability of such collectively moving elastic states. To this end, we determine corresponding fluctuation spectra. They indicate that collectively excitable modes exist in the migrating solid. Differences arise when compared to those of corresponding passive solids. We provide evidence that the modes of excitation associated with the intrinsic fluctuations are related to corresponding modes of entropy production. Overall, we hope to stimulate by our investigation future experimental studies that focus on excitations in active solids.

cond-mat.soft↗

arXiv2024

Rotational dynamics of a disk in a thin film of weakly nematic fluid subject to linear friction

Dynamics at low Reynolds numbers experiences recent revival in the fields of biophysics and active matter. While in bulk isotropic fluids it is exhaustively studied, this is less so in anisotropic fluids and in confined situations. Here, we combine the latter two by studying the rotation of a disk-like inclusion in a uniaxially anisotropic, globally oriented, incompressible two-dimensional fluid film. In terms of a perturbative expansion in parameters that quantify anisotropies in viscosity and in additional linear friction with a supporting substrate or other type of confinement, we derive analytical expressions for the resulting hydrodynamic flow and pressure fields as well as for the resistance and mobility coefficients of the rotating disk. It turns out that, in contrast to translational motion, the solutions remain well-behaved also in the absence of the additional linear friction. Comparison with results from finite-element simulations show very good agreement with those from our analytical calculations. Besides applications to describe technological systems, for instance, in the area of microfluidics and thin cells of aligned nematic liquid crystals, our solutions are important for quantitative theoretical approaches to fluid membranes and thin films in general featuring a preferred direction.

cond-mat.soft↗

arXiv2024

Analytical expressions for the two basic modes of surface displacement and overall deformation of a free-standing or elastically embedded sphere

Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a homogeneous, isotropic, linearly elastic sphere. The modes under consideration correspond to overall changes in volume and to relative uniaxial elongation or contraction. Both situations of an elastic sphere embedded under no-slip conditions in a linearly elastic, homogeneous, isotropic, infinitely extended background medium and of a free-standing elastic sphere are considered. For example, our analytical expressions are important as a basis for computational material optimization in the context of spherical soft actuators.

cond-mat.soft↗