Tanja Schilling - Academia.edu (original) (raw)

Papers by Tanja Schilling

Journal of Chemical Physics, Aug 16, 2016

Journal of statistical physics, Mar 5, 2024

arXiv (Cornell University), Apr 16, 2015

We discuss the crystallization process from the supersaturated melt in terms of its nonequilibriu... more We discuss the crystallization process from the supersaturated melt in terms of its nonequilibrium 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.

Journal of Statistical Physics, Dec 18, 2018

We study the Intermediate Scattering Function (ISF) of the strongly-nonlinear Fermi-Pasta Ulam Mo... more We study the Intermediate Scattering Function (ISF) of the strongly-nonlinear Fermi-Pasta Ulam Model at thermal equilibrium, using both numerical and analytical methods. From the molecular dynamics simulations we distinguish two limit regimes, as the system behaves as an ideal gas at high temperature and as a harmonic chain for low excitations. At intermediate temperatures the ISF relaxes to equilibrium in a nontrivial fashion. We then calculate analytically the Taylor coefficients of the ISF to arbitrarily high orders (the specific, simple shape of the two-body interaction allows us to derive an iterative scheme for these.) The results of the recursion are in good agreement with the numerical ones. Via an estimate of the complete series expansion of the scattering function, we can reconstruct within a certain temperature range its coarse-grained dynamics. This is governed by a memory-dependent Generalized Langevin Equation (GLE), which can be derived via projection operator techniques. Moreover, by analyzing the first series coefficients of the ISF, we can extract a parameter associated to the strength of the memory effects in the dynamics.

arXiv (Cornell University), Sep 28, 2019

We study the statistics of the classical and the quantum Fermi-Pasta-Ulam chain in thermal equili... more We study the statistics of the classical and the quantum Fermi-Pasta-Ulam chain in thermal equilibrium. We construct a numerical scheme that allows us to analyze localization in short chains. The approach is also suited for a structural analysis of arbitrary subsystems of the degrees of freedom, by effectively integrating out the rest of the system. At low temperatures we observe a systematic increase in mobility of the chain when transitioning from classical to quantum mechanics, due to the critical role of dispersion in the latter case.

Connectivity percolation is the transition in which isolated clusters of solid particles in a flu... more Connectivity percolation is the transition in which isolated clusters of solid particles in a fluid (or of voids in a solid) become connected in some sense to form a system - spanning network. This network has a significant effect on the mechanical and transport properties of the material on a macroscopic scale. If, for example, an electrically insulating polymer is mixe d with conductive fibres such as carbon nanotubes, the conductivity of the composite increases by ten or more orders of magnitude near the percolation transition of the filler material. We discuss percolation in suspensions of fibres and of platelets and p resent results from computer simulations as well as connectedness percolation theory. For fibres, our study covers the entire range of aspect ratios from spheres to extremely slender rods. Theory and simulations agree very well for aspect ratios down to va lues as low as 10. The percolation threshold for both hard and ideal 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 of ten used as a rule of thumb for fibres in composite materials. Hence, most fibres that are currently used as fillers in composite materials cannot be regarded as practically infinitely slender from the point of view of percolation theory.

EPL, Oct 1, 2016

PACS 05.10.Ln-Monte Carlo methods PACS 05.10.Gg-Stochastic analysis methods PACS 89.20.-a-Interdi... more PACS 05.10.Ln-Monte Carlo methods PACS 05.10.Gg-Stochastic analysis methods PACS 89.20.-a-Interdisciplinary applications of physics Abstract-We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulation. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude that the state space consists of several pockets between which transitions are rare. Skilled players explore an even smaller subset of positions that populate some of these pockets only very sparsely. These results suggest that the usual measures to estimate both, the size of the state space and the size of the tree of legal moves, are not unique indicators of the complexity of the game, but that topological considerations are equally important. 1 Our analysis of chess also serves to demonstrate the versatility and power of SPRES as a technique that applies to abstract nonphysical dynamics.

Bulletin of the American Physical Society, 2018

We discuss the crystal nucleation pathway of a suspension of monodisperse hard spheres focusing o... more We discuss the crystal nucleation pathway of a suspension of monodisperse hard spheres focusing on the importance of density fluctuations prior to the nucleation event. We contrast time series of density fluctuations at different wavelengths with time series of the commonly considered structural order parameter, which is the size of the largest cluster of adjacent particles having significant hexagonal bond order measured using the method of q6q6 spherical harmonic products. We find that significant density fluctuations take place prior to the structural rearrangements, and suggest that these early drivers of nucleation have previously been overlooked as they are suppressed or relaxed by the structural rearrangements accompanying the formation of the nascent nucleus. The ensemble of nucleating trajectories studied was generated using forward flux sampling at low supersaturation.

Journal of Chemical Physics, May 7, 2019

Complex microscopic many-body processes are often interpreted in terms of so-called "reaction coo... more Complex microscopic many-body processes are often interpreted in terms of so-called "reaction coordinates", i.e. in terms of the evolution of a small set of coarse-grained observables. A rigorous method to produce the equation of motion of such observables is to use projection operator techniques, which split the dynamics of the observables into a main contribution and a marginal one. The basis of any derivation in this framework is the classical (or quantum) Heisenberg equation for an observable. If the Hamiltonian of the underlying microscopic dynamics and the observable under study do not explicitly depend on time, this equation is obtained by a straightforward derivation. However, the problem is more complicated if one considers Hamiltonians which depend on time explicitly as e.g. in systems under external driving, or if the observable of interest has an explicit dependence on time. We use an analogy to fluid dynamics to derive the classical Heisenberg picture and then apply a projection operator formalism to derive the non-stationary generalized Langevin equation for a coarse-grained variable. We show, in particular, that the results presented for timeindependent Hamiltonians and observables in J. Chem. Phys. 147, 214110 (2017) can be generalized to the time-dependent case.

European Physical Journal E, 2001

We investigate the dynamical behavior of lamellar phases in ternary amphiphilic systems of water,... more We investigate the dynamical behavior of lamellar phases in ternary amphiphilic systems of water, oil and amphiphile. The interaction between the amphiphilic monolayers is described by the steric interaction due to thermal fluctuations for uncharged, and by electrostatic interactions for charged systems. The dynamics of the system is determined by the hydrodynamics of the fluid layers. The basic parameters of our model are the viscosities of the two solvents, the average thicknesses of the oil and water layers, and the bending rigidity. The model allows to consider different monolayer interactions across the oil and water layers. Relaxation rates are calculated for arbitrary wave vectors parallel and perpendicular to the average monolayer plane. We find that there is a quite complex crossover behavior from a q 2 law for small parallel wave vectors to a q 3 law for large q. We discuss the relevance of our result for the interpretation of dynamic light-scattering and neutron-spin-echo experiments for these systems.

Nanoscale, 2016

Binary mixtures of nanoparticles self-assemble in the confinement of evaporating oil droplets and... more Binary mixtures of nanoparticles self-assemble in the confinement of evaporating oil droplets and form regular supraparticles. We demonstrate that moderate pressure differences on the order of 100 kPa change the particles' self-assembly behavior. Crystalline superlattices, Janus particles, and core-shell particle arrangements form in the same dispersions when changing the working pressure or the surfactant that sets the Laplace pressure inside the droplets. Molecular dynamics simulations confirm that pressuredependent interparticle potentials affect the self-assembly route of the confined particles. Optical spectrometry, small-angle X-ray scattering and electron microscopy are used to compare experiments and simulations and confirm that the onset of self-assembly depends on particle size and pressure. The overall formation mechanism reminds of the demixing of binary alloys with different phase diagrams.

Journal of Chemical Physics, Aug 5, 2014

We discuss the growth process of a crystalline phase out of a metastable over-compressed liquid t... more 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.

Journal of Chemical Physics, Jun 9, 2016

We investigate the early part of the crystal nucleation process in the hard sphere fluid using da... more 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.

EPL, Sep 18, 2008

We present evidence from computer simulations for glassy dynamics in suspensions of monodisperse ... more We present evidence from computer simulations for glassy dynamics in suspensions of monodisperse hard ellipsoids. In equilibrium, almost spherical ellipsoids show a first-order transition from an isotropic phase to a rotator phase. When overcompressing the isotropic phase into the rotator regime, we observe super-Arrhenius slowing-down of diffusion and relaxation, accompanied by two-step relaxation in positional and orientational correlators. The effects are strong enough for asymptotic laws of mode-coupling theory to apply. Glassy dynamics are unusual in monodisperse systems. Typically, polydispersity in size, a mixture of particle species or networkforming covalent bonds are prerequisite to prevent crystallization. Here, we show that a slight particle anisometry acts as a sufficient source of disorder. This sheds new light on the question of which ingredients are required for glass formation.

Physical Review Letters, Jul 8, 2010

We report on a large scale computer simulation study of crystal nucleation in hard spheres. Throu... more We report on a large scale computer simulation study of crystal nucleation in hard spheres. Through a combined analysis of real and reciprocal space data, a picture of a two-step crystallization process is supported: First dense, amorphous clusters form which then act as precursors for the nucleation of well-ordered crystallites. This kind of crystallization process has been previously observed in systems that interact via potentials that have an attractive as well as a repulsive part, most prominently in protein solutions. In this context the effect has been attributed to the presence of metastable fluid-fluid demixing. Our simulations, however, show that a purely repulsive system (that has no metastable fluid-fluid coexistence) crystallizes via the same mechanism.

Physical Review Letters, Feb 25, 2004

We report on a Monte Carlo study of the pathway for crystal nucleation in a fluid of short, hard,... more We report on a Monte Carlo study of the pathway for crystal nucleation in a fluid of short, hard, colloidal rods. In the earliest stages of nucleation, a single-layered lamellar crystallite forms. Subsequent thickening of this lamella is hampered by the fact that the top and bottom surfaces of the crystallite are preferentially covered by rods that align parallel to the surface. As a single lamella is thermodynamically not stable, subsequent growth of individual crystals is stunted. Recently experimental evidence for such stunted crystal growth has been reported by Maeda and Maeda (2003 Phys. Rev. Lett. 90 018303) for experiments on suspensions of colloidal rods.