arXiv subjects

Sebastian C. Kapfer

Publications and source records attributed to Sebastian C. Kapfer.

At least 19 recordsLinked to original sources

arXiv2020

papaya2: 2D Irreducible Minkowski Tensor computation

A common challenge in scientific and technical domains is the quantitative description of geometries and shapes, e.g. in the analysis of microscope imagery or astronomical observation data. Frequently, it is desirable to go beyond scalar shape metrics such as porosity and surface to volume ratios because the samples are anisotropic or because direction-dependent quantities such as conductances or elasticity are of interest. Minkowski Tensors are a systematic family of versatile and robust higher-order shape descriptors that allow for shape characterization of arbitrary order and promise a path to systematic structure-function relationships for direction-dependent properties. Papaya2 is a software to calculate 2D higher-order shape metrics with a library interface, support for Irreducible Minkowski Tensors and interpolated marching squares. Extensions to Matlab, JavaScript and Python are provided as well. While the tensor of inertia is computed by many tools, we are not aware of other open-source software which provides higher-rank shape characterization in 2D.

cs.GR↗

arXiv2019

Phasonic Diffusion and Self-confinement of Decagonal Quasicrystals in Hyperspace

We introduce a novel simulation method that is designed to explore fluctuations of the phasonic degrees of freedom in decagonal colloidal quasicrystals. Specifically, we attain and characterise thermal equilibrium of the phason ensemble via Monte Carlo simulations with particle motions restricted to elementary phasonic flips. We find that, at any temperature, the random tiling ensemble is strongly preferred over the minimum phason-strain quasicrystal. Phasonic flips are the dominant carriers of diffusive mass transport in physical space. Sub-diffusive transients suggest cooperative flip behaviour on short time scales. In complementary space, particle mobility is geometrically restricted to a thin ring around the acceptance domain, resulting in self-confinement and persistent phasonic order.

cond-mat.soft↗

arXiv2019

Non-equilibrium steady states, coexistence and criticality in driven quasi-two-dimensional granular matter

Nonequilibrium steady states of vibrated inelastic frictionless spheres are investigated in quasi-two-dimensional confinement via molecular dynamics simulations. The phase diagram in the density-amplitude plane exhibits a fluidlike disordered and an ordered phase with threefold symmetry, as well as phase coexistence between the two. A dynamical mechanism exists that brings about metastable traveling clusters and at the same time stable clusters with anisotropic shapes at low vibration amplitude. Moreover, there is a square bilayer state which is connected to the fluid by BKTHNY-type two-step melting with an intermediate tetratic phase. The critical behavior of the two continuous transitions is studied in detail. For the fluid-tetratic transition, critical exponents of $\tildeγ=1.73$, $η_4 \approx 1/4$, and $z=2.05$ are obtained.

cond-mat.soft↗

arXiv2018

A kinetic-Monte Carlo perspective on active matter

We study non-equilibrium phases for interacting two-dimensional self-propelled particles with isotropic pair-wise interactions using a persistent kinetic Monte Carlo (MC) approach. We establish the quantitative phase diagram, including the motility-induced phase separation (MIPS) that is a commonly observed collective phenomena in active matter. In addition, we demonstrate for several different potential forms the presence of two-step melting, with an intermediate hexatic phase, in regions far from equilibrium. Increased activity can melt a two-dimensional solid and the melting lines remain disjoint from MIPS. We establish this phase diagram for a range of the inter-particle potential stiffnesses, and identify the MIPS phase even in the hard-disk limit. We establish that the full description of the phase behavior requires three independent control parameters.

cond-mat.soft↗

arXiv2018

Thermodynamic phases in two-dimensional active matter

Active matter has been intensely studied for its wealth of intriguing properties such as collective motion, motility-induced phase separation (MIPS), and giant fluctuations away from criticality. However, the precise connection of active materials with their equilibrium counterparts has remained unclear. For two-dimensional (2D) systems, this is also because the experimental and theoretical understanding of the liquid, hexatic, and solid equilibrium phases and their phase transitions is very recent. Here, we use self-propelled particles with inverse-power-law repulsions (but without alignment interactions) as a minimal model for 2D active materials. A kinetic Monte Carlo (MC) algorithm allows us to map out the complete quantitative phase diagram. We demonstrate that the active system preserves all equilibrium phases, and that phase transitions are shifted to higher densities as a function of activity. The two-step melting scenario is maintained. At high activity, a critical point opens up a gas-liquid MIPS region. We expect that the independent appearance of two-step melting and of MIPS is generic for a large class of two-dimensional active systems.

cond-mat.stat-mech↗

arXiv2018

Quantum criticality of two-dimensional quantum magnets with long-range interactions

We study the critical breakdown of two-dimensional quantum magnets in the presence of algebraically decaying long-range interactions by investigating the transverse-field Ising model on the square and triangular lattice. This is achieved technically by combining perturbative continuous unitary transformations with classical Monte Carlo simulations to extract high-order series for the one-particle excitations in the high-field quantum paramagnet. We find that the unfrustrated systems change from mean-field to nearest-neighbor universality with continuously varying critical exponents, while the system remains in the universality class of the nearest-neighbor model in the frustrated cases independent of the long-range nature of the interaction.

cond-mat.str-el↗

arXiv2018

Irreversible local Markov chains with rapid convergence towards equilibrium

We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heatbath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric simple exclusion process (TASEP), and by a faster variant (lifted TASEP) that we propose here. Lifted Markov chains and the recently introduced factorized Metropolis acceptance rule extend the irreversible Markov chains discussed here to general pair interactions and to higher dimensions.

cond-mat.stat-mech↗

arXiv2016

Cuddling Ellipsoids: Densest local structures of uniaxial ellipsoids

Connecting the collective behavior of disordered systems with local structure on the particle scale is an important challenge, for example in granular and glassy systems. Compounding complexity, in many scientific and industrial applications, particles are polydisperse, aspherical or even of varying shape. Here, we investigate a generalization of the classical kissing problem in order to understand the local building blocks of packings of aspherical grains. We numerically determine the densest local structures of uniaxial ellipsoids by minimizing the Set Voronoi cell volume around a given particle. Depending on the particle aspect ratio, different local structures are observed and classified by symmetry and Voronoi coordination number. In extended disordered packings of frictionless particles, knowledge of the densest structures allows to rescale the Voronoi volume distributions onto the single-parameter family of $k$-Gamma distributions. Moreover, we find that approximate icosahedral clusters are found in random packings, while the optimal local structures for more aspherical particles are not formed.

cond-mat.soft↗

arXiv2016

Cell-veto Monte Carlo algorithm for long-range systems

We present a rigorous efficient event-chain Monte Carlo algorithm for long-range interacting particle systems. Using a cell-veto scheme within the factorized Metropolis algorithm, we compute each single-particle move with a fixed number of operations. For slowly decaying potentials such as Coulomb interactions, screening line charges allow us to take into account periodic boundary conditions. We discuss the performance of the cell-veto Monte Carlo algorithm for general inverse-power-law potentials, and illustrate how it provides a new outlook on one of the prominent bottlenecks in large-scale atomistic Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2016

Splitting of the universality class of anomalous transport in crowded media

We investigate the emergence of subdiffusive transport by obstruction in continuum models for molecular crowding. While the underlying percolation transition for the accessible space displays universal behavior, the dynamic properties depend in a subtle non-universal way on the transport through narrow channels. At the same time, the different universality classes are robust with respect to introducing correlations in the obstacle matrix as we demonstrate for quenched hard-sphere liquids as underlying structures. Our results confirm that the microscopic dynamics can dominate the relaxational behavior even at long times, in striking contrast to glassy dynamics.

cond-mat.stat-mech↗

arXiv2015

Non-universal Voronoi cell shapes in amorphous ellipsoid packings

In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse local structure metrics derived from the Voronoi diagram of configurations of oblate ellipsoids, for various aspect ratios $α$ and global volume fractions $ϕ_g$. We focus on jammed static configurations of frictional ellipsoids, obtained by tomographic imaging and by discrete element method simulations. In particular, we consider the local packing fraction $ϕ_l$, defined as the particle's volume divided by its Voronoi cell volume. We find that the probability $P(ϕ_l)$ for a Voronoi cell to have a given local packing fraction shows the same scaling behaviour as function of $ϕ_g$ as observed for random sphere packs. Surprisingly, this scaling behaviour is further found to be independent of the particle aspect ratio. By contrast, the typical Voronoi cell shape, quantified by the Minkowski tensor anisotropy index $β=β_0^{2,0}$, points towards a significant difference between random packings of spheres and those of oblate ellipsoids. While the average cell shape $β$ of all cells with a given value of $ϕ_l$ is very similar in dense and loose jammed sphere packings, the structure of dense and loose ellipsoid packings differs substantially such that this does not hold true. This non-universality has implications for our understanding of jamming of aspherical particles.

cond-mat.soft↗

arXiv2015

Liquid-solid transitions in the three-body hard-core model

We determine the phase diagram for a generalisation of two-and three-dimensional hard spheres: a classical system with three-body interactions realised as a hard cut-off on the mean-square distance for each triplet of particles. Quantum versions of this model are important in the context of the unitary Bose gas, which is currently under close theoretical and experimental scrutiny. In two dimensions, the three-body hard-core model possesses a conventional atomic liquid phase and a peculiar solid phase formed by dimers. These dimers interact effectively as hard disks. In three dimensions, the solid phase consists of isolated atoms that arrange in a simple-hexagonal lattice.

cond-mat.stat-mech↗

arXiv2015

2D Melting: From Liquid-Hexatic Coexistence to Continuous Transitions

The phase diagram of two-dimensional continuous particle systems is studied using Event-Chain Monte Carlo. For soft disks with repulsive power-law interactions $\propto r^{-n}$ with $n \gtrsim 6$, the recently established hard-disk melting scenario ($n \to \infty$) holds: a first-order liquid-hexatic and a continuous hexatic-solid transition are identified. Close to $n = 6$, the coexisting liquid exhibits very long orientational correlations, and positional correlations in the hexatic are extremely short. For $n\lesssim 6$, the liquid-hexatic transition is continuous, with correlations consistent with the Kosterlitz-Thouless-Halperin-Nelson-Yong (KTHNY) scenario. To illustrate the generality of these results, we demonstrate that Yukawa particles likewise may follow either the KTHNY or the hard-disk melting scenario, depending on the Debye-Hückel screening length as well as on the temperature.

cond-mat.stat-mech↗

arXiv2013

Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps

In this article, we present an event-driven algorithm that generalizes the recent hard-sphere event-chain Monte Carlo method without introducing discretizations in time or in space. A factorization of the Metropolis filter and the concept of infinitesimal Monte Carlo moves are used to design a rejection-free Markov-chain Monte Carlo algorithm for particle systems with arbitrary pairwise interactions. The algorithm breaks detailed balance, but satisfies maximal global balance and performs better than the classic, local Metropolis algorithm in large systems. The new algorithm generates a continuum of samples of the stationary probability density. This allows us to compute the pressure and stress tensor as a byproduct of the simulation without any additional computations.

cond-mat.stat-mech↗

arXiv2013

Percolation transition by random vertex splitting of diamond networks?

We propose a statistical model defined on the three-dimensional diamond network where the splitting of randomly selected nodes leads to a spatially disordered network, with decreasing degree of connectivity. The terminal state, that is reached when all nodes have been split, is a dense configuration of self-avoiding walks on the diamond network. Starting from the crystallographic diamond network, each of the four-coordinated nodes is replaced with probability p by a pair of two edges, each connecting a pair of the adjacent vertices. For all values of 0 <= p <= 1 the network percolates, yet the fraction fp of the system that belongs to a percolating cluster drops sharply at pc=1 to a finite value. This transition has the signature of a phase transition with scaling exponents for p close to pc that are different from the critical exponents of the second-order phase transition of standard percolation models. As is the case for percolation transitions, this transition significantly affects the mechanical properties of linear-elastic realisations, obtained by replacing edges with solid circular struts to give an effective density phi. Finite element methods demonstrate that, as a low-density cellular structure, the bulk modulus K shows a cross-over from a compression-dominated behaviour (with K proportional to phi) at p=0 to a bending-dominated behaviour (with quadratic dependence of K on phi) at p=1.

cond-mat.dis-nn↗

arXiv2013

Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences.

cond-mat.soft↗

arXiv2013

Sampling from a polytope and hard-disk Monte Carlo

The hard-disk problem, the statics and the dynamics of equal two-dimensional hard spheres in a periodic box, has had a profound influence on statistical and computational physics. Markov-chain Monte Carlo and molecular dynamics were first discussed for this model. Here we reformulate hard-disk Monte Carlo algorithms in terms of another classic problem, namely the sampling from a polytope. Local Markov-chain Monte Carlo, as proposed by Metropolis et al. in 1953, appears as a sequence of random walks in high-dimensional polytopes, while the moves of the more powerful event-chain algorithm correspond to molecular dynamics evolution. We determine the convergence properties of Monte Carlo methods in a special invariant polytope associated with hard-disk configurations, and the implications for convergence of hard-disk sampling. Finally, we discuss parallelization strategies for event-chain Monte Carlo and present results for a multicore implementation.

cond-mat.stat-mech↗

arXiv2012

Shortcomings of the Bond Orientational Order Parameters for the Analysis of Disordered Particulate Matter

Local structure characterization with the bond-orientational order parameters q4, q6, ... introduced by Steinhardt et al. has become a standard tool in condensed matter physics, with applications including glass, jamming, melting or crystallization transitions and cluster formation. Here we discuss two fundamental flaws in the definition of these parameters that significantly affect their interpretation for studies of disordered systems, and offer a remedy. First, the definition of the bond-orientational order parameters considers the geometrical arrangement of a set of neighboring spheres NN(p) around a given central particle p; we show that procedure to select the spheres constituting the neighborhood NN(p) can have greater influence on both the numerical values and qualitative trend of ql than a change of the physical parameters, such as packing fraction. Second, the discrete nature of neighborhood implies that NN(p) is not a continuous function of the particle coordinates; this discontinuity, inherited by ql, leads to a lack of robustness of the ql as structure metrics. Both issues can be avoided by a morphometric approach leading to the robust Minkowski structure metrics ql'. These ql' are of a similar mathematical form as the conventional bond-orientational order parameters and are mathematically equivalent to the recently introduced Minkowski tensors [Europhys. Lett. 90, 34001 (2010); Phys. Rev. E. 85, 030301 (2012)].

cond-mat.soft↗