arXiv subjects

Hartmut Löwen

Publications and source records attributed to Hartmut Löwen.

At least 127 records · Page 7Linked to original sources

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

Tunable critical Casimir forces counteract Casimir-Lifshitz attraction

Casimir forces in quantum electrodynamics emerge between microscopic metallic objects because of the confinement of the vacuum electromagnetic fluctuations occurring even at zero temperature. Their generalization at finite temperature and in material media are referred to as Casimir--Lifshitz forces. These forces are typically attractive, leading to the widespread problem of stiction between the metallic parts of micro- and nanodevices. Recently, repulsive Casimir forces have been experimentally realized but their reliance on specialized materials prevents their dynamic control and thus limits their further applicability. Here, we experimentally demonstrate that repulsive critical Casimir forces, which emerge in a critical binary liquid mixture upon approaching the critical temperature, can be used to actively control microscopic and nanoscopic objects with nanometer precision. We demonstrate this by using critical Casimir forces to prevent the stiction caused by the Casimir--Lifshitz forces. We study a microscopic gold flake above a flat gold-coated substrate immersed in a critical mixture. Far from the critical temperature, stiction occurs because of dominant Casimir--Lifshitz forces. Upon approaching the critical temperature, however, we observe the emergence of repulsive critical Casimir forces that are sufficiently strong to counteract stiction. This experimental demonstration can accelerate the development of micro- and nanodevices by preventing stiction as well as providing active control and precise tunability of the forces acting between their constituent parts.

cond-mat.soft↗

arXiv2022

Brownian particles driven by spatially periodic noise

We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can be integrated formally exactly. We determine the short- and long-time behaviour of the mean displacement (MD) and mean-squared displacement (MSD). In particular we find a very slow dynamics for the mean displacement, scaling as $t^{-1/2}$ with time $t$. Placed under an additional external periodic force near the critical tilt value we compute the stationary current obtained from the corresponding Fokker-Planck equation and identify an essential singularity if the minimum of the noise strength is zero. Finally, in order to further elucidate the effect of the random periodic driving on the diffusion process, we introduce a phase factor in the spatial noise with respect to the external periodic force and identify the value of the phase shift for which the random force exerts its strongest effect on the long-time drift velocity and diffusion coefficient.

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↗

arXiv2022

The Parental Active Model: a unifying stochastic description of self-propulsion

We propose a new overarching model for self-propelled particles that flexibly generates a full family of "descendants". The general dynamics introduced in this paper, which we denote as "parental" active model (PAM), unifies two special cases commonly used to describe active matter, namely active Brownian particles (ABPs) and active Ornstein-Uhlenbeck particles (AOUPs). We thereby document the existence of a deep and close stochastic relationship between them, resulting in the subtle balance between fluctuations in the magnitude and direction of the self-propulsion velocity. Besides illustrating the relation between these two common models, the PAM can generate additional offspring, interpolating between ABP and AOUP dynamics, that could provide more suitable models for a large class of living and inanimate active matter systems, possessing characteristic distributions of their self-propulsion velocity. Our general model is evaluated in the presence of a harmonic external confinement. For this reference example, we present a two-state phase diagram which sheds light on the transition in the shape of the positional density distribution, from a unimodal Gaussian for AOUPs to a Mexican-hat-like profile for ABPs.

cond-mat.soft↗

arXiv2021

Collective self-optimization of communicating active particles

The quest on how to collectively self-organize in order to maximize the survival chances of the members of a social group requires finding an optimal compromise between maximizing the well-being of an individual and that of the group. Here we develop a minimal model describing active individuals which consume or produce, and respond to a shared resource, such as the oxygen concentration for aerotactic bacteria or the temperature field for penguins, while urging for an optimal resource value. Notably, this model can be approximated by an attraction-repulsion model, but in general it features many-body interactions. While the former prevents some individuals from closely approaching the optimal value of the shared resource field, the collective many-body interactions induce aperiodic patterns, allowing the group to collectively self-optimize. Arguably, the proposed optimal-field-based collective interactions represent a generic concept at the interface of active matter physics, collective behavior, and microbiological chemotaxis. This concept might serve as a useful ingredient to optimize ensembles of synthetic active agents or to help unveiling aspects of the communication rules which certain social groups use to maximize their survival chances.

cond-mat.soft↗

arXiv2021

Dynamics of active particles with space-dependent swim velocity

We study the dynamical properties of an active particle subject to a swimming speed explicitly depending on the particle position. The oscillating spatial profile of the swim velocity considered in this paper takes inspiration from experimental studies based on Janus particles whose speed can be modulated by an external source of light. We suggest and apply an appropriate model of an active Ornstein Uhlenbeck particle to the present case. This allows us to predict the stationary properties, by finding the exact solution of the steady-state probability distribution of particle position and velocity. From this, we obtain the spatial density profile and show that its form is consistent with the one found in the framework of other popular models. The reduced velocity distribution highlights the emergence of non-Gaussianity in our generalized AOUP model which becomes more evident as the spatial dependence of the velocity profile becomes more pronounced. Then, we focus on the time-dependent properties of the system. Velocity autocorrelation functions are studied in the steady-state combining numerical and analytical methods derived under suitable approximations. We observe a non-monotonic decay in the temporal shape of the velocity autocorrelation function which depends on the ratio between the persistence length and the spatial period of the swim velocity. Finally, we numerically and analytically study the mean square displacement and the long-time diffusion coefficient. The ballistic regime, observed in the small-time region, is deeply affected by the properties of the swim velocity landscape which induces also a crossover to a sub-ballistic but superdiffusive regime for intermediate times. Finally, the long-time diffusion coefficient decreases as the amplitude of the swim velocity oscillations increases because the diffusion is determined by those regions where the particles are slow.

cond-mat.soft↗

arXiv2021

Anomalous cooling and overcooling of active systems

The phenomenon that a system at a hot temperature cools faster than at a warm temperature, referred to as the Mpemba effect, has been recently realized for trapped colloids. Here, we investigate the cooling and heating process of a self-propelling active colloid using numerical simulations and theoretical calculations with a model that can directly be tested in experiments. Upon cooling the particles' active motion induces a Mpemba effect. Transiently the system can even exhibit smaller temperatures than its final temperature, a surprising phenomenon which we refer to as activity-induced overcooling.

cond-mat.soft↗

arXiv2021

Brownian magneto-gyrator as a tunable microengine

A Brownian particle performs gyrating motion around a potential energy minimum when subjected to thermal noises from two different heat baths. Here, we propose a magneto-gyrator made of a single charged Brownian particle that is steered by an external magnetic field. Key properties, such as the direction of gyration, the torque exerted by the engine on the confining potential and the maximum power delivered by the microengine can be tuned by varying the strength and direction of the applied magnetic field. Further tunability is obtained by rotating the potential in the plane perpendicular to the direction of the magnetic filed. We show that in this generic scenario, the microengine can be stalled and even reversed by the magnetic field. Finally, we highlight a property of the magneto-gyrator that has no counterpart in the overdamped approximation--the heat loss from the hot to cold bath requires explicit knowledge of the mass of the particle. Consequently, the efficiency of the microengine is mass-dependent even in the overdamped limit.

cond-mat.stat-mech↗

arXiv2021

Topology of orientational defects in confined smectic liquid crystals

We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization, this charge is distributed in point-like units of quarter-integer magnitude, which we identify with tetratic disclinations located at the end points and nodes. This coexisting nematic and tetratic order is analyzed with the help of extensive Monte Carlo simulations for a broad range of two-dimensional confining geometries as well as colloidal experiments, showing how the observed defect networks can be universally reconstructed from simple building blocks. We further find that the curvature of the confining wall determines the anchoring behavior of grain boundaries, such that the number of nodes in the emerging networks and the location of their end points can be tuned by changing the number and smoothness of corners, respectively.

cond-mat.soft↗

arXiv2021

Active droploids

Active matter comprises self-driven units, such as bacteria and synthetic microswimmers, that can spontaneously form complex patterns and assemble into functional microdevices. These processes are possible thanks to the out-of-equilibrium nature of active-matter systems, fueled by a one-way free-energy flow from the environment into the system. Here, we take the next step in the evolution of active matter by realizing a two-way coupling between active particles and their environment, where active particles act back on the environment giving rise to the formation of superstructures. In experiments and simulations we observe that, under light-illumination, colloidal particles and their near-critical environment create mutually-coupled co-evolving structures. These structures unify in the form of active superstructures featuring a droplet shape and a colloidal engine inducing self-propulsion. We call them active droploids -- a portmanteau of droplet and colloids. Our results provide a pathway to create active superstructures through environmental feedback.

cond-mat.soft↗

arXiv2021

Active Ornstein-Uhlenbeck model for self-propelled particles with inertia

Self-propelled particles, which convert energy into mechanical motion, exhibit inertia if they have a macroscopic size or move inside a gaseous medium, in contrast to micron-sized overdamped particles immersed in a viscous fluid. Here we study an extension of the active Ornstein-Uhlenbeck model, in which self-propulsion is described by colored noise, to access these inertial effects. We summarize and discuss analytical solutions of the particle's mean-squared displacement and velocity autocorrelation function for several settings ranging from a free particle to various external influences, like a linear or harmonic potential and coupling to another particle via a harmonic spring. Taking into account the particular role of the initial particle velocity in a nonstationary setup, we observe all dynamical exponents between zero and four. After the typical intertial time, determined by the particle's mass, the results inherently revert to the behavior of an overdamped particle with the exception of the harmonically confined systems, in which the overall displacement is enhanced by inertia. We further consider an underdamped model for an active particle with a time-dependent mass, which critically affects the displacement in the intermediate time-regime. Most strikingly, for a sufficiently large rate of mass accumulation, the particle's motion is completely governed by inertial effects as it remains superdiffusive for all times.

cond-mat.soft↗

arXiv2021

Steady azimuthal flow field induced by a rotating sphere near a rigid disk or inside a gap between two coaxially positioned rigid disks

Geometric confinements play an important role in many physical and biological processes and significantly affect the rheology and behavior of colloidal suspensions at low Reynolds numbers. On the basis of the linear Stokes equations, we investigate theoretically and computationally the viscous azimuthal flow induced by the slow rotation of a small spherical particle located in the vicinity of a rigid no-slip disk or inside a gap between two coaxially positioned rigid no-slip disks of the same radius. We formulate the solution of the hydrodynamic problem as a mixed-boundary-value problem in the whole fluid domain, which we subsequently transform into a system of dual integral equations. Near a stationary disk, we show that the resulting integral equation can be reduced into an elementary Abel integral equation that admits a unique analytical solution. Between two coaxially positioned stationary disks, we demonstrate that the flow problem can be transformed into a system of two Fredholm integral equations of the first kind. The latter are solved by means of numerical approaches. Using our solution, we further investigate the effect of the disks on the slow rotational motion of a colloidal particle and provide expressions of the hydrodynamic mobility as a function of the system geometry. We compare our results with corresponding finite-element simulations and observe very good agreement.

physics.flu-dyn↗

arXiv2021

Active Brownian and inertial particles in disordered environments: short-time expansion of the mean-square displacement

We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square-displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behaviour adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher order powers in time for the MSD. Finally, for inertial particles two superballistic regimes are found where the scaling exponent of the MSD with time is $α=3$ and $α=4$. We confirm our theoretical predictions by computer simulations. Moreover they are verifiable in experiments on self-propelled colloids in random environments.

cond-mat.soft↗

arXiv2021

Active noise-driven particles under space-dependent friction in one dimension

We study a Langevin equation describing the stochastic motion of a particle in one dimension with coordinate $x$, which is simultaneously exposed to a space-dependent friction coefficient $γ(x)$, a confining potential $U(x)$ and non-equilibrium (i.e., active) noise. Specifically, we consider frictions $γ(x)=γ_0 + γ_1 | x |^p$ and potentials $U(x) \propto | x |^n$ with exponents $p = 1,2$ and $n = 0, 1, 2$. We provide analytical and numerical results for the particle dynamics for short times and the stationary probability density functions (PDFs) for long times. The short-time behaviour displays diffusive and ballistic regimes while the stationary PDFs display unique characteristic features depending on the exponent values $(p, n)$. The PDFs interpolate between Laplacian, Gaussian and bimodal distributions, whereby a change between these different behaviours can be achieved by a tuning of the friction strengths ratio $γ_0/γ_1$. Our model is relevant for molecular motors moving on a one-dimensional track and can also be realized for confined self-propelled colloidal particles.

cond-mat.soft↗

arXiv2021

Barrier-mediated predator-prey dynamics

The survival chance of a prey chased by a predator depends not only on their relative speeds but importantly also on the local environment they have to face. For example, a wolf chasing a deer might take a long time to cross a river which can quickly be crossed by the deer. Here, we propose a simple predator-prey model for a situation in which both the escaping prey and the chasing predator have to surmount an energetic barrier. Different barrier-assisted states of catching or final escaping are classified and suitable scaling laws separating these two states are derived. We discuss the effect of fluctuations on the catching times and determine states in which catching or escaping is more likely. We further identify trapping or escaping states which are determined by hydrodynamics and chemotactic interactions. Our results are of importance for both microbes and self-propelled unanimate microparticles following each other by non-reciprocal interactions in inhomogeneous landscapes.

cond-mat.soft↗

arXiv2021

Time-dependent inertia of self-propelled particles: the Langevin rocket

Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics which involve inertia, friction and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation are manifold ranging from minirockets which are self-propelled by burning their own mass, dust particles in plasma which lose mass by evaporating material to walkers with expiring activity. Here we present analytical solutions for several dynamical correlation functions such as the mean-square displacement and the orientational and velocity autocorrelation functions. If the parameters exhibit a slow power-law in time, we obtain anomalous superdiffusion with a non-trivial dynamical exponent. Finally we constitute the "Langevin rocket" model by including orientational fluctuations in the traditional Tsiolkovsky rocket equation. We calculate the mean reach of the Langevin rocket and discuss different mass ejection strategies to maximize it. Our results can be tested in experiments on macroscopic robotic or living particles or in self-propelled mesoscopic objects moving in media of low viscosity such as complex plasma.

cond-mat.soft↗

arXiv2021

Dynamical density functional theory for "dry" and "wet" active matter

In the last 50 years, equilibrium density functional theory (DFT) has been proven to be a powerful, versatile and predictive approach for the statics and structure of classical particles. This theory can be extended to the nonequilibrium dynamics of completely overdamped Brownian colloidal particles towards so-called dynamical density functional theory (DDFT). The success of DDFT makes it a promising candidate for a first-principle description of active matter. In this lecture, we shall first recapitulate classical DDFT for passive colloidal particles typically described by Smoluchowski equation. After a basic derivation of DDFT from the Smoluchowski equation, we discuss orientational degrees of freedom and the effect of hydrodynamic interactions for passive particles. This brings us into an ideal position to generalize DDFT towards active matter. In particular we distinguish between "dry active matter" which is composed of self-propelled particles that contain no hydrodynamic flow effects of a surrounding solvent and "wet active matter" where the hydrodynamic flow fields generated by the microswimmers are taken into account. For the latter, DDFT is a tool which unifies thermal fluctuations, direct particle interactions, external driving fields and hydrodynamic effects arising from internal self-propulsion discriminating between "pushers" and "pullers". A number of recent applications is discussed including transient clustering of self-propelled rods and the spontaneous formation of a hydrodynamic pump in confined microswimmers.

cond-mat.soft↗