arXiv subjects

Tanja Schilling

Publications and source records attributed to Tanja Schilling.

At least 55 records · Page 3Linked to original sources

arXiv2016

Clearing out a maze: The hungry random walker and its anomalous diffusion

We study chemotaxis in a porous medium using as a model a biased ("hungry") random walk on a percolating cluster. In close resemblance to the 1980s arcade game Pac-Man, the hungry random walker consumes food, which is initially distributed in the maze, and biases its movement towards food-filled sites. We observe that, on the percolating cluster, the mean-squared displacement of the pacman process shows anomalous dynamics, which follow a power law with a dynamical exponent different from both that of a self avoiding random walk as well as that of an unbiased random walk. The change in dynamics with the propensity to move towards food is well described by a dynamical exponent that depends continuously on this propensity, and results in slower differential growth when compared to the unbiased random walk.

cond-mat.stat-mech↗

arXiv2016

The Early Crystal Nucleation Process in Hard Spheres shows Synchronised Ordering and Densification

We investigate the early part of the crystal nucleation process in the hard sphere fluid using data produced by computer simulation. We find that hexagonal order manifests continuously in the overcompressed liquid, beginning approximately one diffusion time before the appearance of the first `solid-like' particle of the nucleating cluster, and that a collective influx of particles towards the nucleation site occurs simultaneously to the ordering process: the density increases leading to nucleation are generated by the same individual particle displacements as the increases in order. We rule out the presence of qualitative differences in the early nucleation process between medium and low overcompressions, and also provide evidence against any separation of translational and orientational order on the relevant lengthscales.

cond-mat.soft↗

arXiv2015

Connectivity Percolation in Suspensions of Attractive Square-Well Spherocylinders

We have studied the connectivity percolation transition in suspensions of attractive square-well spherocylinders by means of Monte Carlo simulation and connectednes percolation theory. In the 1980s the percolation threshold of slender fibres has been predicted to scale as the fibres' inverse aspect ratio (Phys.~Rev.~B {\bf 30}, 3933 (1984)). The main finding of our study is that the attractive spherocylinder system reaches this inverse scaling regime at much lower aspect ratios than found in suspensions of hard spherocylinders. We explain this difference by showing that third virial corrections of the pair connectedness functions, which are responsible for the deviation from the scaling regime, are less important for attractive potentials than for hard particles.

cond-mat.soft↗

arXiv2015

Percolation in suspensions of hard nanoparticles: From spheres to needles

We investigate geometric percolation and scaling relations in suspensions of nanorods, covering the entire range of aspect ratios from spheres to extremely slender needles. A new version of connectedness percolation theory is introduced and tested against specialized Monte Carlo simulations. The theory accurately predicts percolation thresholds for aspect ratios as low as 10. The percolation threshold for rod-like particles of aspect ratios below 1000 deviates significantly from the inverse aspect ratio scaling prediction, thought to be valid in the limit of infinitely slender rods and often used as a rule of thumb for nano-fibers in composite materials. Hence, most fibers that are currently used as fillers in composite materials cannot be regarded as practically infinitely slender for the purposes of percolation theory. Comparing percolation thresholds of hard rods and new benchmark results for ideal rods, we find that (i) for large aspect ratios, they differ by a factor that is inversely proportional to the connectivity distance between the hard cores, and (ii) they approach the slender rod limit differently.

cond-mat.soft↗

arXiv2015

Percolation in suspensions of polydisperse hard rods : quasi-universality and finite-size effects

We present a study of connectivity percolation in suspensions of hard spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. We focus attention on polydispersity in the length, the diameter and the connectedness criterion, and invoke bimodal, Gaussian and Weibull distributions for these. The main finding from our simulations is that the percolation threshold shows quasi universal behaviour, i.e., to a good approximation it depends only on certain cumulants of the full size and connectivity distribution. Our connectedness percolation theory hinges on a Lee-Parsons type of closure recently put forward that improves upon the often-used second virial approximation [ArXiv e-prints, May 2015, 1505.07660]. The theory predicts exact universality. Theory and simulation agree quantitatively for aspect ratios in excess of 20, if we include the connectivity range in our definition of the aspect ratio of the particles. We further discuss the mechanism of cluster growth that, remarkably, differs between systems that are polydisperse in length and in width, and exhibits non-universal aspects.

cond-mat.soft↗

arXiv2015

Dissipation in a Crystallization Process

We discuss the crystallization process from the supersaturated melt in terms of its non-equilibrium properties. In particular, we quantify the amount of heat that is produced irreversibly when a suspension of hard spheres crystallizes. This amount of heat can be interpreted as arising from the resistance of the system against undergoing phase transition. We identify an intrinsic compression rate that separates a quasi-static regime from a regime of rapid crystallization. In the former the disspated heat grows linearly in the compression rate. In the latter the system crystallizes more easily, because new relaxation channels are opened, at the cost of forming a higher fraction of non-equilibrium crystal structures. In analogy to a shear-thinning fluid, the system shows a decreased resistance when it is driven rapidly.

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↗

arXiv2014

Crystal nucleation mechanism in melts of short polymer chains under quiescent conditions and under shear flow

We present a molecular dynamics simulation study of crystal nucleation from undercooled melts of n-alkanes, and we identify the molecular mechanism of homogeneous crystal nucleation under quiescent conditions and under shear flow. We compare results for n-eicosane(C20) and n-pentacontahectane(C150), i.e. one system below the entanglement length and one above. Under quiescent conditions, we observe that entanglement does not have an effect on the nucleation mechanism. For both chain lengths, the chains first align and then straighten locally. Then the local density increases and finally positional ordering sets in. At low shear rates the nucleation mechanism is the same as under quiescent conditions, while at high shear rates the chains align and straighten at the same time. We report on the effects of shear rate and temperature on the nucleation rates and estimate the critical shear rates, beyond which the nucleation rates increase with the shear rate. We show that the viscosity of the system is not affected by the crystalline nuclei.

cond-mat.soft↗

arXiv2014

Crystal growth from a supersaturated melt: relaxation of the solid-liquid dynamic stiffness

We discuss the growth process of a crystalline phase out of a metastable over-compressed liquid that is brought into contact with a crystalline substrate. The process is modeled by means of molecular dynamics. The particles interact via the Lennard-Jones potential and their motion is locally thermalized by Langevin dynamics. We characterize the relaxation process of the solid-liquid interface, showing that the growth speed is maximal for liquid densities above the solid coexistence density, and that the structural properties of the interface rapidly converge to equilibrium-like properties. In particular, we show that the off-equilibrium dynamic stiffness can be extracted using capillary wave theory arguments, even if the growth front moves fast compared to the typical diffusion time of the compressed liquid, and that the dynamic stiffness converges to the equilibrium stiffness in times much shorter than the diffusion time.

cond-mat.soft↗

arXiv2014

Strong Effect of Weak Charging in Suspensions of Anisotropic Colloids

Suspensions of hard colloidal particles frequently serve as model systems in studies on fundamental aspects of phase transitions. But often colloidal particles that are considered as ``hard'' are in fact weakly charged. If the colloids are spherical, weak charging has a only a weak effect on the structural properties of the suspension, which can be easily corrected for. However, this does not hold for anisotropic particles. We introduce a model for the interaction potential between charged ellipsoids of revolution (spheroids) based on the Derjaguin approximation of Debye--Hückel Theory and present a computer simulation study on aspects of the system's structural properties and phase behaviour. In line with previous experimental observations, we find that even a weak surface charge has a strong impact on the correlation functions. A likewise strong impact is seen on the phase behaviour, in particular, we find stable cubatic order in suspensions of oblate ellipsoids.

cond-mat.soft↗

arXiv2014

Solid phase properties and crystallization in simple model systems

We review theoretical and simulational approaches to the description of equilibrium bulk crystal and interface properties as well as to the nonequilibrium processes of homogeneous and heterogeneous crystal nucleation for the simple model systems of hard spheres and Lennard-Jones particles. For the equilibrium properties of bulk and interfaces, density functional theories employing fundamental measure functionals prove to be a precise and versatile tool, as exemplified with a closer analysis of the hard sphere crystalliquid interface. A detailed understanding of the dynamic process of nucleation in these model systems nevertheless still relies on simulational approaches. We review bulk nucleation and nucleation at structured walls and examine in closer detail the influence of walls with variable strength on nucleation in the Lennard-Jones fluid. We find that a planar crystalline substrate induces the growth of a crystalline film for a large range of lattice spacings and interaction potentials. Only a strongly incommensurate substrate and a very weakly attractive substrate potential lead to crystal growth with a non-zero contact angle.

cond-mat.soft↗

arXiv2013

Crystallization mechanism in melts of short n-alkane chains

We study crystallization in a model system for eicosane (C20) by means of molecular dynamics simulation and we identify the microscopic mechanisms of homogeneous crystal nucleation and growth. For the nucleation process, we observe that chains first align and then straighten. Then the local density increases and finally the monomer units become ordered positionally. The subsequent crystal growth process is characterized by a sliding-in motion of the chains. Chains preferably attach to the crystalline cluster with one end and then move along the stems of already crystallized chains towards their final position. This process is cooperative, i.e. neighboring chains tend to get attached in clusters rather than independently

cond-mat.soft↗

arXiv2013

Influence of random pinning on the crystallization process in suspensions of hard spheres

We discuss crystal formation in supersaturated suspensions of monodisperse hard spheres with a concentration of hard spheres randomly pinned in space and time. The pinning procedure introduces an external length scale and an external time scale that restrict the accessible number of configurations and ultimately the number of pathways leading to crystallization. We observe a significant drop in the nucleation rate density at a characteristic pinning concentration that can be directly related to the structure of the critical nucleus and the dynamics of its formation in the unpinned system.

cond-mat.stat-mech↗

arXiv2013

Crystallization in Glassy Suspensions of Hard Ellipsoids

We have carried out computer simulations of overcompressed suspensions of hard monodisperse ellipsoids and observed their crystallization dynamics. The system was compressed very rapidly in order to reach the regime of slow, glass-like dynamics. We find that, although particle dynamics become sub-diffusive and the intermediate scattering function clearly develops a shoulder, crystallization proceeds via the usual scenario: nucleation and growth for small supersaturations, spinodal decomposition for large supersaturations. In particular, we compared the mobility of the particles in the regions where crystallization set in with the mobility in the rest of the system. We did not find any signature in the dynamics of the melt that pointed towards the imminent crystallization events.

cond-mat.soft↗

arXiv2013

Solvent hydrodynamics speed up crystal nucleation in suspensions of hard spheres

We present a computer simulation study on the crystal nucleation process in suspensions of hard spheres, fully taking into account the solvent hydrodynamics. If the dynamics of collodial crystallization were purely diffusive, the crystal nucleation rate densities would drop as the inverse of the solvent viscosity. However, we observe that the nucleation rate densities do not scale in this way, but are enhanced at high viscosities. This effect might explain the large discrepancy between the nuclation rate densities obtained by simulation and experiment that have reported in the literature so far.

cond-mat.soft↗

arXiv2013

Euclidean Upgrade from a Minimal Number of Segments

In this paper, we propose an algebraic approach to upgrade a projective reconstruction to a Euclidean one, and aim at computing the rectifying homography from a minimal number of 9 segments of known length. Constraints are derived from these segments which yield a set of polynomial equations that we solve by means of Gröbner bases. We explain how a solver for such a system of equations can be constructed from simplified template data. Moreover, we present experiments that demonstrate that the given problem can be solved in this way.

cs.CV↗

arXiv2012

Free Energies by Thermodynamic Integration Relative to an Exact Solution, Used to Find the Handedness-Switching Salt Concentration for DNA

Sets of free energy differences are useful for finding the equilibria of chemical reactions, while absolute free energies have little physical meaning. However finding the relative free energy between two macrostates by subtraction of their absolute free energies is a valuable strategy in certain important cases. We present calculations of absolute free energies of biomolecules, using a combination of the well-known Einstein Molecule method (for treating the solute) with a conceptually related method of recent genesis for computing free energies of liquids (to treat the solvent and counterions). The approach is based on thermodynamic integration from a detailed atomistic model to one which is simplified but analytically solvable, thereby giving the absolute free energy as that of the tractable model plus a correction term found numerically. An example calculation giving the free energy with respect to salt concentration for the B- and Z-isomers of all-atom duplex DNA in explicit solvent and counterions is presented. The coexistence salt concentration is found with unprecedented accuracy.

cond-mat.stat-mech↗

arXiv2012

Connectivity percolation in suspensions of hard platelets

We present a study on connectivity percolation in suspensions of hard platelets by means of Monte Carlo simulation. We interpret our results using a contact-volume argument based on an effective single--particle cell model. It is commonly assumed that the percolation threshold of anisotropic objects scales as their inverse aspect ratio. While this rule has been shown to hold for rod-like particles, we find that for hard plate-like particles the percolation threshold is non-monotonic in the aspect ratio. It exhibits a shallow minimum at intermediate aspect ratios and then saturates to a constant value. This effect is caused by the isotropic-nematic transition pre-empting the percolation transition. Hence the common strategy to use highly anisotropic, conductive particles as fillers in composite materials in order to produce conduction at low filler concentration is expected to fail for plate-like fillers such as graphene and graphite nanoplatelets.

cond-mat.soft↗