arXiv subjects

René Wittmann

Publications and source records attributed to René Wittmann.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical density functional theory for dense odd-diffusive fluids

Odd diffusion breaks time-reversal symmetry in overdamped systems through transverse probability currents while preserving equilibrium steady states. In this work, we develop a dynamical density functional theory (DDFT) for dense interacting odd-diffusive fluids and apply it to ultrasoft particles in two dimensions. In bulk, odd diffusion qualitatively reshapes collective relaxation by generating transient circulating current patterns which do not exist in normal fluids. Under harmonic ring confinement, the circulation of probability current induces an angular redistribution of density along the ring during relaxation. This unique footprint of odd diffusion opens up a shorter pathway to equilibrium. Repulsive interactions significantly enhance these effects. Excellent agreement with Brownian dynamics simulations confirms that our odd-DDFT framework quantitatively captures all essential nonequilibrium aspects of the nontrivial odd transport and collective redistribution for dense fluids in both bulk and confined geometries.

cond-mat.soft↗

arXiv2025

Nascent biofilms on soft surfaces

Soft surfaces, spanning vastly different environmental and biomedical settings, are frequently colonised by surface-associated bacteria. Yet, how soft surfaces govern bacterial dynamics and their self-organisation into colonies remains poorly understood. Using experiments and agent-based modelling, we report the self-organisation of bacterial cells into nascent biofilms on soft substrates. By tuning the elastic modulus over two orders of magnitude, we show that the colony morphology, spreading dynamics and collective behaviour depend on the substrate stiffness, wherein softer surfaces promote slowly expanding, geometrically anisotropic, multilayered colonies, while harder substrates drive rapid, isotropic expansion of bacterial monolayers before multilayer structures emerge. Supported a cell mechanical model and two-dimensional agent-based simulations, our results identify that anisotropic drag forces on soft substrates, emerging due to local deformations, underpin colony anisotropy and swift verticalisation. In contrast, reduced drag on hard surfaces allows rapid expansion of monolayers, thus delaying the transition to a multilayer structure. Surface compliance, a key but overlooked determinant of early-stage biofilm development, could be harnessed to engineer biofilm structures and dynamics for nature-inspired and biomedical applications.

physics.bio-ph↗

arXiv2025

Biaxial nematic order in fundamental measure theory

Liquid crystals consisting of biaxial particles can exhibit a much richer phase behavior than their uniaxial counterparts. Usually, one has to rely on simulation results to understand the phase diagram of these systems, since very few analytical results exist. In this work, we apply fundamental measure theory, which allows us to derive free energy functionals for hard particles from first principles and with high accuracy, to systems of hard cylinders, cones and spherotriangles. We provide a general recipe for incorporating biaxial liquid crystal order parameters into fundamental measure theory and use this framework to obtain the phase boundaries for the emergence of orientational order in the considered systems. Our results provide insights into the phase behavior of biaxial nematic liquid crystals and, in particular, into methods for their analytical investigation.

cond-mat.soft↗

arXiv2025

Confined active particles with spatially dependent Lorentz force: an odd twist to the "best Fokker-Planck approximation"

We derive a version of the so-called "best Fokker-Planck approximation" (BFPA) to describe the spatial properties of interacting active Ornstein-Uhlenbeck particles (AOUPs) in arbitrary spatial dimensions. In doing so, we also take into account the odd-diffusive contribution of the Lorentz force acting on a charged particle in a spatially dependent magnetic field, sticking to the overdamped limit. While the BFPA itself does not turn out to be widely useful, our general approach allows to deduce an appropriate generalization of the Fox approximation, which we use to characterize the stationary behavior of a single active particle in an external potential by deriving analytic expressions for configurational probability distributions (or effective potentials). In agreement with computer simulations, our theory predicts that the Lorentz force reduces the effective attraction and thus the probability to find an active particle in the vicinity of a repulsive wall. Even for an inhomogeneous magnetic field, our theoretical findings provide useful qualitative insights, specifically regarding the location of accumulation regions.

cond-mat.soft↗

arXiv2025

Foundation of classical dynamical density functional theory: uniqueness of time-dependent density-potential mappings

When can we map a classical density profile to an external potential? In equilibrium, without time dependence, the one-body density is known to specify the external potential that is applied to the many-body system. This mapping from a density to the potential is the cornerstone of classical density functional theory (DFT). Here, we consider non-equilibrium, time-dependent many-body systems that evolve from a given initial condition. We derive explicit conditions, for example, no flux at the boundary, that ensure that the mapping from the density to a time-dependent external potential is unique. We thus prove the underlying assertion of dynamical density functional theory (DDFT), without resorting to the so-called adiabatic approximation often used in applications. By ascertaining uniqueness for all $n$-body densities, we ensure that the proof and the physical conclusions drawn from it hold for general superadiabatic dynamics of interacting systems even in the presence of (known) non-conservative forces.

math-ph↗

arXiv2025

Dynamical field theories for biaxial liquid crystals

Phase field crystal (PFC) models constitute central tools for a microscopic understanding of the dynamics of complex systems in soft matter physics. They have found widespread application in the modeling of the uniaxial orientational ordering of liquid crystals. However, only very limited progress has been made in applying them to the more complex cases of biaxial phases and biaxial particles. Here, we discuss the microscopic derivation of PFC models for biaxial liquid crystals. We illustrate it by presenting two models, one involving four scalar orientational order parameters relevant for the dynamics of biaxial particles, and one involving two scalar order parameters and a director field to describe biaxial phases in a three-dimensional uniaxial nematic liquid crystal. These models allow for an efficient simulation of spatially inhomogeneous biaxial orientational ordering dynamics. We also combine a microscopic and macroscopic approach to extract model coefficients for a full biaxial model from the microscopic derivation for a simple special case. This universal method also enables to perform derivations for other low-symmetry particles where, due to the complexity of the general case, this has not been previously attempted.

cond-mat.soft↗

arXiv2024

A Hitchhiker's Guide To Active Motion

Intelligent decisions in response to external informative input can allow organisms to achieve their biological goals while spending very little of their own resources. In this paper, we develop and study a minimal model for a navigational task, performed by an otherwise completely motorless particle that possesses the ability of \textit{hitchhiking} in a bath of active Brownian particles (ABPs). Hitchhiking refers to identifying and attaching to suitable surrounding bath particles. Using a reinforcement learning algorithm, such an agent, which we refer to as intelligent hitchhiking particle (IHP), is enabled to persistently navigate in the desired direction. This relatively simple IHP can also anticipate and react to characteristic motion patterns of their hosts, which we exemplify for a bath of chiral ABPs (cABPs). To demonstrate that the persistent motion of the IHP will outperform that of the bath particles in view of long-time ballistic motion, we calculate the mean-squared displacement and discuss its dependence on the density and persistence time of the bath ABPs by means of an analytic model.

cond-mat.soft↗

arXiv2024

Layer topology of smectic grain boundaries

Grain boundaries in extremely confined colloidal smectics possess a topological fine structure with coexisting nematic and tetratic symmetry of the director field. An alternative way to approach the problem of smectic topology is via the layer structure, which is typically more accessible in experiments on molecular liquid crystals. Here, we consider exemplary density functional theory results for two-dimensional hard rods to illustrate how the concept of endpoint defects, which appear as tetratic disclinations of quarter charge in director topology, translates to smectic layer topology built around the networks formed by density maxima and minima. By doing so, we elaborate on further advantages of a topological concept evolving around the layer structure rather than the director field, such as providing insight in the structure of edge dislocations or virtual defects at the confining walls.

cond-mat.soft↗

arXiv2023

Collective mechano-response dynamically tunes cell-size distributions in growing bacterial colonies

Mechanical stresses stemming from environmental factors are a key determinant of cellular behavior and physiology. Yet, the role of self-induced biomechanical stresses in growing bacterial colonies has remained largely unexplored. Here, we demonstrate how collective mechanical forcing plays an important role in the dynamics of the cell size of growing bacteria. We observe that the measured elongation rate of well-nourished \textit{Escherichia coli} cells decreases over time, depending on the free area around each individual, and associate this behavior with the response of the growing cells to mechanical stresses. Via a cell-resolved model accounting for the feedback of collective forces on individual cell growth, we quantify the effect of this mechano-response on the structure and composition of growing bacterial colonies, including the local environment of each cell. Finally, we predict that a mechano-cross-response between competing bacterial strains with distinct growth rates affects their size distributions.

cond-mat.soft↗

arXiv2023

Emergent memory from tapping collisions in active granular matter

In an equilibrium thermal environment, random elastic collisions between background particles and a tracer establish the picture of Brownian motion fulfilling the celebrated Einstein relation between diffusivity and mobility. In nature, environments often comprise collections of autonomously moving objects that exhibit fascinating non-equilibrium phenomena and are nowadays termed active matter. We investigate experimentally the impact of an active background on a passive tracer using vibrationally excited active particles. They produce multiple correlated tapping collisions with the tracer, for which a persistent memory emerges in the dynamics. The system is described by a generalized active Einstein relation that constrains fluctuations, dissipation, and effective activity, by taking the emerging tracer memory into account. Since the resulting persistence can largely be tuned by the environmental density and motility, our findings can be useful to engineer properties of various active systems in biomedical applications, microfluidics, chemical engineering, or swarm robotics.

cond-mat.stat-mech↗

arXiv2023

Colloidal smectics in button-like confinements: experiment and theory

Liquid crystals can self-organize into a layered smectic phase. While the smectic layers are typically straight forming a lamellar pattern in bulk, external confinement may drastically distort the layers due to the boundary conditions imposed on the orientational director field. Resolving this distortion leads to complex structures with topological defects. Here, we explore the configurations adopted by two-dimensional colloidal smectics made from nearly hard rod-like particles in complex confinements, characterized by a button-like structure with two internal boundaries (inclusions): a two-holed disk and a double annulus. The topology of the confinement generates new structures which we classify in reference to previous work as generalized laminar and generalized Shubnikov states. To explore these configurations, we combine particle-resolved experiments on colloidal rods with three complementary theoretical approaches: Monte-Carlo simulation, first-principles density functional theory and phenomenological $\mathbf{Q}$-tensor modeling. This yields a consistent and comprehensive description of the structural details. In particular, we characterize a nontrivial tilt angle between the direction of the layers and symmetry axes of the confinement.

cond-mat.soft↗

arXiv2023

Statistics of carrier-cargo complexes

We explore the statistics of assembling soft-matter building blocks to investigate the uptake and encapsulation of cargo particles by carriers engulfing their load. While the such carrier-cargo complexes are important for many applications out of equilibrium, such as drug delivery and synthetic cell encapsulation, we uncover here the basic statistical physics in minimal hard-core-like models for particle uptake. Introducing an exactly solvable equilibrium model in one dimension, we demonstrate that the formation of carrier-cargo complexes can be largely tuned by both the cargo concentration and the carriers' interior size. These findings are intuitively explained by interpreting the internal free space (partition function) of the cargo inside a carrier as its engulfment strength, which can be mapped to an external control parameter (chemical potential) of an additional effective particle species. Assuming a hard carrier membrane, such a mapping can be exactly applied to account for multiple cargo uptake involving various carrier or cargo species and even attractive uptake mechanisms, while soft interactions require certain approximations. We further argue that the Boltzmann occupation law identified within our approach is broken when particle uptake is governed by non-equilibrium forces. Speculating on alternative occupation laws using effective parameters, we put forward a Bose-Einstein-like phase transition associated with polydisperse carrier properties.

cond-mat.soft↗

arXiv2023

Network topology of interlocked chiral particles

Self-assembly of chiral particles with an L-shape is explored by Monte-Carlo computer simulations in two spatial dimensions. For sufficiently high packing densities in confinement, a carpet-like texture emerges due to the interlocking of L-shaped particles, resembling a distorted smectic liquid crystalline layer pattern. From the positions of either of the two axes of the particles, two different types of layers can be extracted, which form distinct but complementary entangled networks. These coarse-grained network structures are then analyzed from a topological point of view. We propose a global charge conservation law by using an analogy to uniaxial smectics and show that the individual network topology can be steered by both confinement and particle geometry. Our topological analysis provides a general classification framework for applications to other intertwined dual networks.

cond-mat.soft↗

arXiv2023

Dynamics of active particles with translational and rotational inertia

Inertial effects affecting both the translational and rotational dynamics are inherent to a broad range of active systems at the macroscopic scale. Thus, there is a pivotal need for proper models in the framework of active matter to correctly reproduce experimental results, hopefully achieving theoretical insights. For this purpose, we propose an inertial version of the active Ornstein-Uhlenbeck particle (AOUP) model accounting for particle mass (translational inertia) as well as its moment of inertia (rotational inertia) and derive the full expression for its steady-state properties. The inertial AOUP dynamics introduced in this paper is designed to capture the basic features of the well-established inertial active Brownian particle (ABP) model, i.e., the persistence time of the active motion and the long-time diffusion coefficient. For a small or moderate rotational inertia, these two models predict similar dynamics at all timescales and, in general, our inertial AOUP model consistently yields the same trend upon changing the moment of inertia for various dynamical correlation functions.

cond-mat.soft↗

arXiv2022

Density functional approach to elastic properties of three-dimensional dipole-spring models for magnetic gels

Magnetic gels are composite materials, consisting of a polymer matrix and embedded magnetic particles. Those are mechanically coupled to each other, giving rise to the magnetostrictive effects as well as to a controllable overall elasticity responsive to external magnetic fields. Due to their inherent composite and thereby multiscale nature, a theoretical framework bridging different levels of description is indispensable for understanding the magnetomechanical properties of magnetic gels. In this study, we extend a recently developed density functional approach from two spatial dimensions to more realistic three-dimensional systems. Along these lines, we connect a mesoscopic characterization resolving the discrete structure of the magnetic particles, to macroscopic continuum parameters of magnetic gels. In particular, we incorporate the long-range nature of the magnetic dipole-dipole interaction, and consider the approximate incompressibility of the embedding media, and relative rotations with respect to an external magnetic field breaking rotational symmetry. We then probe the shape of the model system in its reference state, confirming the dependence of magnetostrictive effects on the configuration of the magnetic particles and on the shape of the considered sample. Moreover, calculating the elastic and rotational coefficients on the basis of our mesoscopic approach, we examine how the macroscopic types of behavior are related to the mesoscopic properties. Implications for real systems of random particle configurations are also discussed.

cond-mat.soft↗

arXiv2022

Geometric criteria for the absence of effective many-body interactions in nonadditive hard particle mixtures

We consider a mixture of small and big classical particles in arbitrary spatial dimensions interacting via hard-body potentials with non-additive excluded-volume interactions. In particular, we focus on variants of the Asakura--Oosawa (AO) model where the interaction between the small particles is neglected but the big-small and big-big interactions are present and can be condensed into an effective depletion interaction among the big particles alone. The original AO model involves hard spherical particles in three spatial dimensions with interaction diameters $σ_\text{pp}=0$, $σ_\text{cc}>0$ and $σ_\text{pc}>σ_\text{cc}/2$ respectively, where $σ_{ij}$ with $\{i,j\}=\{\text{p},\text{c}\}$ (indicating the physical interpretation of the small and big particles as polymers (p) and colloids (c), respectively) is the minimum possible center-to-center distance between particle $i$ and particle $j$ allowed by the excluded-volume constraints. It is common knowledge that there are only pairwise effective depletion interactions between the big particles if the geometric condition $σ_\text{pc}/σ_\text{cc} < 1/\sqrt{3}$ is fulfilled. In this case, triplet and higher-order many body interactions are vanishing and the equilibrium statistics of the binary mixture can exactly be mapped onto that of an effective one-component system with the effective depletion pair-potential. Here we prove this geometric criterion rigorously and generalize it to polydisperse mixtures and to anisotropic particle shapes in any dimension, providing geometric criteria sufficient to guarantee the absence of triplet and higher-order many body interactions. For an external hard wall confining the full mixture, we also give criteria which guarantee that the system can be mapped onto one with effective external one-body interactions.

math-ph↗

arXiv2022

Active particles driven by competing spatially dependent self-propulsion and external force

We investigate how the competing presence of a nonuniform motility landscape and an external confining field affects the properties of active particles. We employ the active Ornstein-Uhlenbeck particle (AOUP) model with a periodic swim velocity profile to derive analytical approximations for the steady-state probability distribution of position and velocity, encompassing both the Unified Colored Noise Approximation and the theory of potential-free active particles with spatially dependent swim velocity recently developed. We test the theory by confining an active particle in a harmonic trap, which gives rise to interesting properties, such as a transition from a unimodal to a bimodal (and, eventually multimodal) spatial density, induced by decreasing the spatial period of the self propulsion. Correspondingly, the velocity distribution shows pronounced deviations from the Gaussian shape, even displaying a bimodal profile in the high-motility regions. Our results can be confirmed by real-space experiments on active colloidal Janus particles in external fields.

cond-mat.stat-mech↗

arXiv2022

Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals

Observing and characterizing the complex ordering phenomena of liquid crystals subjected to external constraints constitutes an ongoing challenge for chemists and physicists alike. To elucidate the delicate balance appearing when the intrinsic positional order of smectic liquid crystals comes into play, we perform Monte-Carlo simulations of rod-like particles in a range of cavities with a cylindrical symmetry. Based on recent insights into the topology of smectic orientational grain boundaries in two dimensions, we analyze the emerging three-dimensional defect structures from the perspective of tetratic symmetry. Using an appropriate three-dimensional tetratic order parameter constructed from the Steinhardt order parameters, we show that those grain boundaries can be interpreted as a pair of tetratic disclination lines that are located on the edges of the nematic domain boundary. Thereby, we shed light on the fine structure of grain boundaries in three-dimensional confined smectics.

cond-mat.soft↗