Analytical method for reconstructing the stress on a spherical particle from its surface deformation.

The mechanical forces that cells experience from the tissue surrounding them are crucial for their behavior and development. Experimental studies of such mechanical forces require a method for measuring them. A widely used approach in this context is bead deformation analysis, where spherical particles are embedded into the tissue. The deformation of the particles then allows to reconstruct the mechanical stress acting on them. Existing approaches for this reconstruction are either very time-consuming or not sufficiently general. In this article, we present an analytical approach to this problem based on an expansion in solid spherical harmonics that allows us to find the complete stress tensor describing the stress acting on the tissue. Our approach is based on the linear theory of elasticity and uses an ansatz specifically designed for deformed spherical bodies. We clarify the conditions under which this ansatz can be used, making our results useful also for other contexts in which this ansatz is employed. Our method can be applied to arbitrary radial particle deformations and requires a very low computational effort. The usefulness of the method is demonstrated by an application to experimental data.

Pair-distribution function of active Brownian spheres in three spatial dimensions: simulation results and analytical representation.

The pair-distribution function, which provides information about correlations in a system of interacting particles, is one of the key objects of theoretical soft matter physics. In particular, it allows for microscopic insights into the phase behavior of active particles. While this function is by now well studied for two-dimensional active matter systems, the more complex and more realistic case of three-dimensional systems is not well understood by now. In this work, we analyze the full pair-distribution function of spherical active Brownian particles interacting via a Weeks-Chandler-Andersen potential in three spatial dimensions using Brownian dynamics simulations. Besides extracting the structure of the pair-distribution function from the simulations, we obtain an analytical representation for this function, parametrized by activity and concentration, which takes into account the symmetries of a homogeneous stationary state. Our results are useful as input to quantitative models of active Brownian particles and advance our understanding of the microstructure in dense active fluids.

Orientation-Dependent Propulsion of Active Brownian Spheres: From Self-Advection to Programmable Cluster Shapes.

Applications of active particles require a method for controlling their dynamics. While this is typically achieved via direct interventions, indirect interventions based, e.g., on an orientation-dependent self-propulsion speed of the particles, become increasingly popular. In this Letter, we investigate systems of interacting active Brownian spheres in two spatial dimensions with orientation-dependent propulsion using analytical modeling and Brownian dynamics simulations. It is found that the orientation dependence leads to self-advection, circulating currents, and programmable cluster shapes.

Active Brownian particles in external force fields: Field-theoretical models, generalized barometric law, and programmable density patterns.

We investigate the influence of external forces on the collective dynamics of interacting active Brownian particles in two as well as three spatial dimensions. Via explicit coarse graining, we derive predictive models, i.e., models that give a direct relation between the models' coefficients and the bare parameters of the system, that are applicable for space- and time-dependent external force fields. We study these models for the cases of gravity and harmonic traps. In particular, we derive a generalized barometric formula for interacting active Brownian particles under gravity that is valid for low to high concentrations and activities of the particles. Furthermore, we show that one can use an external harmonic trap to induce motility-induced phase separation in systems that, without external fields, remain in a homogeneous state. This finding makes it possible to realize programmable density patterns in systems of active Brownian particles. Our analytic predictions are found to be in very good agreement with Brownian dynamics simulations.

An acoustically controlled helical microrobot.

As a next-generation toolkit, microrobots can transform a wide range of fields, including micromanufacturing, electronics, microfluidics, tissue engineering, and medicine. While still in their infancy, acoustically actuated microrobots are becoming increasingly attractive. However, the interaction of acoustics with microstructure geometry is poorly understood, and its study is necessary for developing next-generation acoustically powered microrobots. We present an acoustically driven helical microrobot with a length of 350 µm and a diameter of 100 µm that is capable of locomotion using a fin-like double-helix microstructure. This microrobot responds to sound stimuli at ~12 to 19 kHz and mimics the spiral motion of natural microswimmers such as spirochetes. The asymmetric double helix interacts with the incident acoustic field, inducing a propulsion torque that causes the microrobot to rotate around its long axis. Moreover, our microrobot has the unique feature of its directionality being switchable by simply tuning the acoustic frequency. We demonstrate this locomotion in 2D and 3D artificial vasculatures using a single sound source.

Dependence of the acoustic propulsion of nano- and microcones on their orientation and aspect ratio.

Recent research revealed the orientation-dependent propulsion of a cone-shaped colloidal particle that is exposed to a planar traveling ultrasound wave. Here, we extend the previous research by considering nano- and microcones with different aspect ratios and studying how the propulsion of a particle depends on its orientation and aspect ratio. We also study how the orientation-averaged propulsion of a cone-shaped particle, which corresponds to an isotropic ultrasound field, depends on its aspect ratio and identify an aspect ratio of 1/2 where the orientation-averaged propulsion is particularly strong. To make our simulation results easier reusable for follow-up research, we provide a corresponding simple analytic representation.

From a microscopic inertial active matter model to the Schrödinger equation.

Active field theories, such as the paradigmatic model known as 'active model B+', are simple yet very powerful tools for describing phenomena such as motility-induced phase separation. No comparable theory has been derived yet for the underdamped case. In this work, we introduce active model I+, an extension of active model B+ to particles with inertia. The governing equations of active model I+ are systematically derived from the microscopic Langevin equations. We show that, for underdamped active particles, thermodynamic and mechanical definitions of the velocity field no longer coincide and that the density-dependent swimming speed plays the role of an effective viscosity. Moreover, active model I+ contains an analog of the Schrödinger equation in Madelung form as a limiting case, allowing one to find analoga of the quantum-mechanical tunnel effect and of fuzzy dark matter in active fluids. We investigate the active tunnel effect analytically and via numerical continuation.

How to derive a predictive field theory for active Brownian particles: a step-by-step tutorial.

The study of active soft matter has developed into one of the most rapidly growing areas of physics. Field theories, which can be developed either via phenomenological considerations or by coarse-graining of a microscopic model, are a very useful tool for understanding active systems. Here, we provide a detailed review of a particular coarse-graining procedure, theinteraction-expansion method(IEM). The IEM allows for the systematic microscopic derivation of predictive field theories for systems of interacting active particles. We explain in detail how it can be used for a microscopic derivation of active model B+, which is a widely used scalar active matter model. Extensions and possible future applications are also discussed.

Thermodynamics of an Empty Box.

A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central object and develops a thermodynamic theory by treating the geometric degrees of freedom of the box as the degrees of freedom of a thermodynamic system. Applying standard mathematical methods to the thermodynamics of an empty box allows equations with the same structure as those of cosmology and classical and quantum mechanics to be derived. The simple model system of an empty box is shown to have interesting connections to classical mechanics, special relativity, and quantum field theory.

Inertial dynamics of an active Brownian particle.

Active Brownian motion commonly assumes spherical overdamped particles. However, self-propelled particles are often neither symmetric nor overdamped yet underlie random fluctuations from their surroundings. Active Brownian motion has already been generalized to include asymmetric particles. Separately, recent findings have shown the importance of inertial effects for particles of macroscopic size or in low-friction environments. We aim to consolidate the previous findings into the general description of a self-propelled asymmetric particle with inertia. We derive the Langevin equation of such a particle as well as the corresponding Fokker-Planck equation. Furthermore, a formula is presented that allows reconstructing the hydrodynamic resistance matrix of the particle by measuring its trajectory. Numerical solutions of the Langevin equation show that, independently of the particle's shape, the noise-free trajectory at zero temperature starts with an inertial transition phase and converges to a circular helix. We discuss this universal convergence with respect to the helical motion that many microorganisms exhibit.

Collective guiding of acoustically propelled nano- and microparticles.

One of the most important potential applications of motile nano- and microdevices is targeted drug delivery. To realize this, biocompatible particles that can be guided collectively towards a target inside a patient's body are required. Acoustically propelled nano- and microparticles constitute a promising candidate for such biocompatible, artificial motile particles. The main remaining obstacle to targeted drug delivery by motile nano- and microdevices is to also achieve a reliable and biocompatible method for guiding them collectively to their target. Here, we propose such a method. As we confirm by computer simulations, it allows for the remote guiding of large numbers of acoustically propelled particles to a prescribed target by combining a space- and time-dependent acoustic field and a time-dependent magnetic field. The method works without detailed knowledge about the particle positions and for arbitrary initial particle distributions. With these features, it paves the way for the future application of motile particles as vehicles for targeted drug delivery in nanomedicine.

Perspective: New directions in dynamical density functional theory.

Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.

Acoustic Propulsion of Nano- and Microcones: Dependence on the Viscosity of the Surrounding Fluid.

This article investigates how the acoustic propulsion of cone-shaped colloidal particles that are exposed to a traveling ultrasound wave depends on the viscosity of the fluid surrounding the particles. Using acoustofluidic computer simulations, we found that the propulsion of such nano- and microcones decreases strongly and even changes sign for increasing shear viscosity. In contrast, we found only a weak dependence of the propulsion on the bulk viscosity. The obtained results are in line with the findings of previous theoretical and experimental studies.

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.

Analytical approach to chiral active systems: Suppressed phase separation of interacting Brownian circle swimmers.

We consider chirality in active systems by exemplarily studying the phase behavior of planar systems of interacting Brownian circle swimmers with a spherical shape. For this purpose, we derive a predictive field theory that is able to describe the collective dynamics of circle swimmers. The theory yields a mapping between circle swimmers and noncircling active Brownian particles and predicts that the angular propulsion of the particles leads to a suppression of their motility-induced phase separation, being in line with recent simulation results. In addition, the theory provides analytical expressions for the spinodal corresponding to the onset of motility-induced phase separation and the associated critical point as well as for their dependence on the angular propulsion of the circle swimmers. We confirm our findings by Brownian dynamics simulations. Agreement between results from theory and simulations is found to be good.

Orientation-Dependent Propulsion of Triangular Nano- and Microparticles by a Traveling Ultrasound Wave.

Previous studies on ultrasound-propelled nano- and microparticles have considered only systems in which the particle orientation is perpendicular to the direction of propagation of the ultrasound. However, in future applications of these particles, they will typically be able to attain other orientations. Therefore, using direct acoustofluidic simulations, here we study how the propulsion of triangular nano- and microparticles, which are known to have a particularly efficient acoustic propulsion and are therefore promising candidates for future applications, depends on their orientation relative to the propagation direction of a traveling ultrasound wave. Our results reveal that the propulsion of the particles depends strongly on their orientation relative to the direction of wave propagation and that the particles tend to orient perpendicularly to the wave direction. We also address the orientation-averaged translational and angular velocities of the particles, which correspond to the particles' effective propulsion for an isotropic exposure to ultrasound. Our results allow assessment of how free ultrasound-propelled colloidal particles move in three spatial dimensions and thus constitute an important step toward the realization of envisaged future applications of such particles.

Pressure Drives Rapid Burst-Like Coordinated Cellular Motion from 3D Cancer Aggregates.

A key behavior observed during morphogenesis, wound healing, and cancer invasion is that of collective and coordinated cellular motion. Hence, understanding the different aspects of such coordinated migration is fundamental for describing and treating cancer and other pathological defects. In general, individual cells exert forces on their environment in order to move, and collective motion is coordinated by cell-cell adhesion-based forces. However, this notion ignores other mechanisms that encourage cellular movement, such as pressure differences. Here, using model tumors, it is found that increased pressure drove coordinated cellular motion independent of cell-cell adhesion by triggering cell swelling in a soft extracellular matrix (ECM). In the resulting phenotype, a rapid burst-like stream of cervical cancer cells emerged from 3D aggregates embedded in soft collagen matrices (0.5 mg mL-1 ). This fluid-like pushing mechanism, recorded within 8 h after embedding, shows high cell velocities and super-diffusive motion. Because the swelling in this model system critically depends on integrin-mediated cell-ECM adhesions and cellular contractility, the swelling is likely triggered by unsustained mechanotransduction, providing new evidence that pressure-driven effects must be considered to more completely understand the mechanical forces involved in cell and tissue movement as well as invasion.

Mori-Zwanzig Formalism for General Relativity: A New Approach to the Averaging Problem.

Cosmology relies on a coarse-grained description of the universe, assumed to be valid on large length scales. However, the nonlinearity of general relativity makes coarse graining extremely difficult. We here address this problem by extending the Mori-Zwanzig projection operator formalism, a highly successful coarse-graining method from statistical mechanics, towards general relativity. Using the Buchert equations, we derive a new dynamic equation for the Hubble parameter which captures the effects of averaging through a memory function. This gives an empirical prediction for the cosmic jerk.

Acoustically propelled nano- and microcones: fast forward and backward motion.

We focus on cone-shaped nano- and microparticles, which have recently been found to show particularly strong propulsion when they are exposed to a traveling ultrasound wave, and study based on direct acoustofluidic computer simulations how their propulsion depends on the cones' aspect ratio. The simulations reveal that the propulsion velocity and even its sign are very sensitive to the aspect ratio, where short particles move forward whereas elongated particles move backward. Furthermore, we identify a cone shape that allows for a particularly large propulsion speed. Our results contribute to the understanding of the propulsion of ultrasound-propelled colloidal particles, suggest a method for separation and sorting of nano- and microcones concerning their aspect ratio, and provide useful guidance for future experiments and applications.

Effects of social distancing and isolation on epidemic spreading modeled via dynamical density functional theory.

For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of describing these effects. In this work, we present an extended model for disease spread based on combining a susceptible-infected-recovered model with a dynamical density functional theory where social distancing and isolation of infected persons are explicitly taken into account. We show that the model exhibits interesting transient phase separation associated with a reduction of the number of infections, and allows for new insights into the control of pandemics.