arXiv subjects

Gerhard Kahl

Publications and source records attributed to Gerhard Kahl.

At least 19 recordsLinked to original sources

arXiv2026

Emergent swimming strategies of a smart three-bead swimmer

Low-Reynolds-number microswimmers have recently attracted much interest for their ubiquity in biology and their applications in biotechnology and medicine. However, a key obstacle for the design and deployment of artificial microswimmers lies in their autonomy: to successfully perform tasks in any real-world scenario, these swimmers need to be able to interact with and adapt to their environment without external control. Here, we train a simple two-dimensional model microswimmer (consisting of three-bead) to learn autonomous swimming strategies via Reinforcement Learning, focusing on neuroevolution techniques to derive controller architectures with minimal complexity. We identify five different, characteristic swimming gaits: three of these gaits lead to directed locomotion with varying grades of efficiency and two gaits result in a rotational, inefficient movement. Remarkably, all of these gaits can be achieved by very simple neural networks (with less than ten nodes and weights), showing that low-Reynolds-number swimming can be achieved efficiently and robustly while requiring only minimal computational power. These results are of particular interest to the experimental design of artificial microswimmers and may have implications for modeling biological microorganisms such as Chlamydomonas reinhardtii.

physics.bio-ph↗

arXiv2026

Radial Distribution Function in a Two Dimensional Core-Shoulder Particle System

An important quantity in liquid state theory is the radial distribution function $g(r)$. It can be calculated within the framework of classical density functional theory in two very distinct ways. In the test-particle route, one fixes a single fluid particle, turning it into an external potential in which the inhomogeneous structure of the fluid is calculated by minimising the functional. The second route to $g(r)$ in density functional theory employs the Ornstein-Zernike equation and the pair direct correlation function, that can be obtained from the second functional derivatives of the excess (over the ideal gas) free energy functional. Since typically an approximate excess free energy functional is employed, the test-particle route, which requires only one functional derivative, is more accurate than the Ornstein-Zernike route. Here we study a two dimensional core-shoulder particle system and find that in some circumstances the results from the Ornstein-Zernike route can be comparable in accuracy to the test-particle results for $r>\sigma$, the core diameter. We also examine in detail the asymptotic $r\to\infty$ decay of $g(r)$, finding a variety of possible decay wavelengths at different state points and state points where there is a crossover from one wavelength to a very different one. This behaviour is a signature pointing to the rich phase behaviour of the incipient solid phases.

cond-mat.soft↗

arXiv2026

Navigating complex phase diagrams in soft matter systems

Colloidal fluids can exhibit complex phase behavior and determining phase diagrams via experiments or computer simulations can be laborious. We demonstrate that the dispersion relation $\omega(k)$, obtained from dynamical density functional theory for the uniform density system, is a highly versatile tool for {\it predicting} where in the phase diagram complex crystals form. The sign of $\omega(k)$ determines whether density modes with wavenumber $k$ grow or decay over time. We demonstrate the predictive power by investigating the complex phase behavior of particles interacting via core-shoulder pair potentials. With complementary Monte Carlo simulations, we show that regions of the phase diagram where $\omega(k)$ has one or several unstable (growing) wavenumbers are also where crystalline phases occur. Going further, by tuning these unstable wavenumbers via the interaction-potential and state-point parameters, we design systems with quasicrystals in the phase diagram. We identify a system with a certain shoulder-range exhibiting at least 10 different phases. Our general approach accelerates considerably the mapping of complex phase diagrams, crucial for the design of new materials.

cond-mat.soft↗

arXiv2025

Static and dynamic properties of a binary, symmetric mixture of ultrasoft particles in the vicinity of criticality

We investigate the static and the dynamic properties of an binary, equimolar, size-symmetric mixture of ultrasoft particles in the vicinity of the critical point of the system. Based on the generalized exponential potential (GEM) of order four for the particle interaction and using extensive molecular dynamics simulations in the canonical ensemble we investigate the above mentioned properties for various scenarios: we consider several super- and subcritical states, we expose the system to rapid quenches and to external shearing forces. Based on an accurate determination of the phase diagram and of the location of the critical point we study the static structure of the system in terms of particle-based radial distribution functions. As systems of GEM particles are prone to cluster formation we complement these investigations by a detailed analysis of the composition of the clusters and of their spatial correlations for the different scenarios introduced above. Furthermore we analyse the temperature dependence of the diffusivity of the particles and of the shear viscosity of the system. All these data provide a detailed and profound insight into the properties of the system under phase separation conditions and near criticality.

cond-mat.soft↗

arXiv2024

Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system

We investigate the phase ordering (pattern formation) of systems of two-dimensional core-shell particles using Monte-Carlo (MC) computer simulations and classical density functional theory (DFT). The particles interact via a pair potential having a hard core and a repulsive square shoulder. Our simulations show that on cooling, the liquid state structure becomes increasingly characterised by long wavelength density modulations, and on further cooling forms a variety of other phases, including clustered, striped and other patterned phases. In DFT, the hard core part of the potential is treated using either fundamental measure theory or a simple local density approximation, whereas the soft shoulder is treated using the random phase approximation. The different DFTs are bench-marked using large-scale grand-canonical-MC and Gibbs-ensemble-MC simulations, demonstrating their predictive capabilities and shortcomings. We find that having the liquid state static structure factor $S(k)$ for wavenumber $k$ is sufficient to identify the Fourier modes governing both the liquid and solid phases. This allows to identify from easier-to-obtain liquid state data the wavenumbers relevant to the periodic phases and to predict roughly where in the phase diagram these patterned phases arise.

cond-mat.soft↗

arXiv2024

Two-stage assembly of patchy ellipses: From bent-core particlesto liquid crystal analogs

We investigate the two-dimensional behavior of colloidal patchy ellipsoids specifically designed to follow a two-step assembly process from the monomer state to mesoscopic liquid-crystal phases, via the formation of so-called bent-core units at the intermediate stage. Our model comprises a binary mixture of ellipses interacting via the Gay-Berne potential and decorated by surface patches, with the binary components being mirror-image variants of each other - referred to as left-handed and right-handed ellipses according to the position of their patches. The surface patches are designed so as in the first stage of the assembly the monomers form bent-cores units, i.e. V-shaped dimers with a specific bent angle. The Gay-Berne interactions, which act between the ellipses, drive the dimers to subsequently form the characteristic phase observed in bent-core liquid crystals. We numerically investigate -- by means of both Molecular Dynamics and Monte Carlo simulations -- the described two-step process: we first optimize a target bent-core unit and we then fully characterize its state diagram in temperature and density, defining the regions where the different liquid crystalline phases dominate.

cond-mat.soft↗

arXiv2024

Phase separation dynamics in a symmetric binary mixture of ultrasoft particles

Phase separation plays an role in determining the self-assembly of biological and soft-matter systems. In biological systems, liquid-liquid phase separation inside a cell leads to the formation of various macromolecular aggregates. The interaction among these aggregates is soft, i.e., these can significantly overlap at a small energy cost. From the computer simulation point of view, these complex macromolecular aggregates are generally modeled by the so-called soft particles. The effective interaction between two particles is defined via the generalized exponential potential (GEM-n) with n = 4. Here, using molecular dynamics simulations, we study the phase separation dynamics of a size-symmetric binary mixture of ultrasoft particles. We find that when the mixture is quenched to a lower temperature below the critical temperature, the two components spontaneously start to separate. Domains of the two components form, and the equal-time order parameter reveals that the domains grow in a power-law manner with exponent 1/3, which is consistent with the Lifshitz-Slyozov law for conserved systems. Further, the static structure factor shows a power-law decay with exponent 4 consistent with the Porod law.

cond-mat.soft↗

arXiv2024

On the Lattice Ground State of Densely Packed Hard Ellipses

Among lattice configurations of densely packed hard ellipses, Monte Carlo simulations are used to identify the so-called parallel and diagonal lattices as the two favourable states. The free energies of these two states are computed for several system sizes employing the Einstein Crystal method. An accurate calculation of the free energy difference between the two states reveals the parallel lattice as the state with lowest free energy. The origin of the entropic difference between the two states is further elucidated by assessing the roles of the translational and rotational degrees of freedom.

cond-mat.soft↗

arXiv2022

Ordered ground state configurations of the asymmetric Wigner bilayer system -- revisited: an unsupervised clustering algorithm analysis

We have re-analysed the rich plethora of ground state configurations of the asymmetric Wigner bilayer system that we had recently published in a related diagram of states [M. Antlanger \textit{et al.}, Phys. Rev. Lett. \textbf{117}, 118002 (2016)], comprising roughly 60~000 state points in the phase space spanned by the distance between the plates and the charge asymmetry parameter of the system. In contrast to this preceding contribution where the classification of the emerging structures was carried out ``by hand'', we have used this time machine learning concepts, notably based on a principal component analysis and a $k$-means clustering approach: using a 30-dimensional feature vector for each emerging structure (containing relevant information, such as the composition of the configuration as well as the most relevant order parameters) we were able to re-analyse these ground state configurations in a considerably more systematic and comprehensive manner than we could possibly do in the previously published classification scheme. Indeed we were now able to identify new structures in previously unclassified regions of the parameter space and could considerably refine the previous classification scheme, identifying thereby a rich wealth of new emerging ground state configurations. Thorough consistency checks confirm the validity of the newly defined diagram of states.

cond-mat.soft↗

arXiv2021

Deformable hard particles particles confined in a disordered porous matrix

With suitably designed Monte Carlo simulations we have investigated the properties of mobile, impenetrable, yet deformable particles that are immersed into a porous matrix, the latter one realized via a frozen configuration of spherical particles. By virtue of a model put forward by Batista and Miller [Phys. Rev. Lett. {\bf 105}, 088305 (2010)] the fluid particles can change under the impact of their surrounding (i.e., either other fluid particles or the matrix) their shape within the class of ellipsoids of revolution; such a change in shape is related to an energy change which is fed into suitably defined selection rules in the deformation "moves" of the Monte Carlo simulations. This concept represents a simple, yet powerful model of realistic, deformable molecules with complex internal structures (such as dendrimers or polymers). For the evaluation of the properties of the system we have used the well-known quenched-annealed protocol (with its characteristic double average prescription) and have analysed the simulation data in terms of static properties (radial distribution function and aspect ratio distribution of the ellipsoids) and dynamic features (notably the mean squared displacement). Our data provide evidence that the degree of deformability of the fluid particles has a distinct impact on the aforementioned properties of the system.

cond-mat.soft↗

arXiv2021

Elasticity in crystals with high density of local defects : insights from ultra-soft colloids

In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a microscopic basis to include and account for the motion of point-defects in an otherwise ordered crystalline structure. We study the elastic properties of a point-defect rich crystal within a first-principles theoretical framework derived from microscopic equations of motion. This framework allows us to make specific predictions pertaining to the mechanical properties which we can validate through deformation experiments performed in Molecular Dynamics simulations.

cond-mat.soft↗

arXiv2021

Microswimmers learning chemotaxis with genetic algorithms

Various microorganisms and some mammalian cells are able to swim in viscous fluids by performing nonreciprocal body deformations, such as rotating attached flagella or by distorting their entire body. In order to perform chemotaxis, i.e. to move towards and to stay at high concentrations of nutrients, they adapt their swimming gaits in a nontrivial manner. We propose a model how microswimmers are able to autonomously adapt their shape in order to swim in one dimension towards high field concentrations using an internal decision making machinery modeled by an artificial neural network. We present two methods to measure chemical gradients, spatial and temporal sensing, as known for swimming mammalian cells and bacteria, respectively. Using the NEAT genetic algorithm surprisingly simple neural networks evolve which control the shape deformations of the microswimmer and allow them to navigate in static and complex time-dependent chemical environments. By introducing noisy signal transmission in the neural network the well-known biased run-and-tumble motion emerges. Our work demonstrates that the evolution of a simple internal decision-making machinery, which we can fully interpret and is coupled to the environment, allows navigation in diverse chemical landscapes. These findings are of relevance for intracellular biochemical sensing mechanisms of single cells, or for the simple nervous system of small multicellular organisms such as C. elegans.

physics.bio-ph↗

arXiv2021

On the yielding of a defect-rich model crystal under shear: insights from molecular dynamics simulations

Point defects in real crystals at finite temperatures are inevitable. Their dynamics severely influence the mechanical properties of crystals under shear giving rise to nonlinear effects such as ductility. Therefore, it is crucial to explore the interplay of the equilibrium point-defect diffusion timescales and shear-induced timescales to understand the plastic deformation of crystals. Using extensive nonequilibrium molecular dynamics simulations, we present a study on the yielding behavior of cluster crystals (CC), an archetypal model for defect-rich crystals where the crystalline structure is characterized by multiple occupancies (cluster) of particles at a lattice site. In equilibrium, particles diffuse via site-to-site hopping keeping the crystalline structure intact. We consider the CCs at a fixed density and different temperatures where it remains in the FCC structure, and the diffusion timescales of particles vary depending on the temperature. We choose the range of shear rates, which covers timescales higher and much lower than the equilibrium diffusion timescales at high temperatures. For the considered range of shear rates and temperatures, both the macro and microscopic responses of CCs to the shear suggest that the yielding scenario remains independent of the diffusion of particles. It involves the plastic deformation of the underlying crystalline structure. The averaged local bond order parameters and local angle measurements demonstrate the structural changes and cooperative movement of the center of masses of the clusters close to the yield point. A comparison with the soft-sphere (SS) FCC crystal reveals the similarities in the yielding behavior of both systems. Nonetheless, diffusion of particles influences certain features, such as a less prominent increase in the local bond order parameters and local angles close to the yield point.

cond-mat.soft↗

arXiv2021

Inverse patchy colloids: synthesis, modeling and self-organization

Inverse patchy colloids are nano- to micro-scale particles with a surface divided into differently charged regions. This class of colloids combines directional, selective bonding with a relatively simple particle design: owing to the competitive interplay between the orientation-dependent attraction and repulsion -- induced by the interactions between like/oppositely charged areas -- experimentally accessible surface patterns are complex enough to favor the stabilization of specific structures of interest. Most important, the behavior of heterogeneously charged units can be ideally controlled by means of external parameters, such as the pH and the salt concentration. We present a concise review about this class of systems, spanning the range from the synthesis of model inverse patchy particles to their self-assembly, covering their coarse-grained modeling and the related numerical/analytical treatments.

cond-mat.soft↗

arXiv2020

On the degeneracy of ordered ground state configurations of the aspherical Gaussian core model

We provide rigorous evidence that the ordered ground state configurations of a system of parallel oriented, ellipsoidal particles, interacting via a Gaussian interaction (termed in literature as Gaussian core nematics) {\it must} be infinitely degenerate: we have demonstrated that these configurations originate from the related ground state configuration of the corresponding symmetric Gaussian core system via a suitable stretching operation of this lattice in combination with an arbitrary rotation. These findings explain related observations in former investigations, which then remained unexplained. Our conclusions have far reaching consequences for the search of ground state configurations of other nematic particles.

cond-mat.soft↗

arXiv2020

Reliable computational prediction of supramolecular ordering of complex molecules under electrochemical conditions

We propose a computationally lean, two-stage approach that reliably predicts self-assembly behavior of complex charged molecules on a metallic surfaces under electrochemical conditions. Stage one uses ab initio simulations to provide reference data for the energies (evaluated for archetypical configurations) to fit the parameters of a conceptually much simpler and computationally less expensive model of the molecules: classical, spherical particles, representing the respective atomic entities, a soft but perfectly conductive wall potential represents the metallic surface. Stage two feeds the energies that emerge from this classical model into highly efficient and reliable optimization techniques to identify via energy minimization the ordered ground state configurations of the molecules. We demonstrate the power of our approach by successfully reproducing, on a semi-quantitative level, the intricate supramolecular ordering observed experimentally for PQP$^+$ and ClO$_4^-$ molecules at an Au(111)-electrolyte interface, including the formation of open-porous, self-hosts--guest, and stratified bilayer phases as a function of the electric field at the solid--liquid interface. We also discuss the role of the perchlorate ions in the self-assembly process, whose positions could not be identified in the related experimental investigations.

physics.comp-ph↗

arXiv2020

Hydrodynamic correlations of viscoelastic fluids by multiparticle collision dynamics simulations

The emergent fluctuating hydrodynamics of a viscoelastic fluid modeled by the multiparticle collision dynamics (MPC) approach is studied. The fluid is composed of flexible, Gaussian phantom polymers, which interact by local momentum-conserving stochastic MPC collisions. For comparison, the analytical solution of the linearized Navier-Stokes equation is calculated, where viscoelasticity is taken into account by a time-dependent shear relaxation modulus. The fluid properties are characterized by the transverse velocity autocorrelation function in Fourier space as well as in real space. Various polymer lengths are considered---from dumbbells to (near-)continuous polymers. Viscoelasticity affects the fluid properties and leads to strong correlations, which overall decay exponentially in Fourier space. In real space, the center-of-mass velocity autocorrelation function of individual polymers exhibits a long-time tail independent of polymer length, which decays as $t^{-3/2}$, similar to a Newtonian fluid, in the asymptotic limit $t \to \infty$. Moreover, for long polymers an additional power-law decay appears at time scales shorter than the longest polymer relaxation time with the same time dependence, but negative correlations, and the polymer length dependence $L^{-1/2}$. Good agreement is found between the analytical and simulation results.

cond-mat.soft↗

arXiv2019

Controlled self-aggregation of polymer-based nanoparticles employing shear flow and magnetic fields

Star polymers with magnetically functionalized end groups are presented as a novel polymeric system whose morphology, self-aggregation, and orientation can easily be tuned by exposing these macromolecules simultaneously to an external magnetic field and to shear forces. Our investigations are based on a specialized simulation technique which faithfully takes into account the hydrodynamic interactions of the surrounding, Newtonian solvent. We find that the combination of magnetic field (including both strength and direction) and shear rate controls the mean number of magnetic clusters, which in turn is largely responsible for the static and dynamic behavior. While some properties are similar to comparable non-magnetic star polymers, others exhibit novel phenomena; examples of the latter include the breakup and reorganization of the clusters beyond a critical shear rate, and a strong dependence of the efficiency with which shear rate is translated into whole-body rotations on the direction of the magnetic field.

cond-mat.soft↗