CeNoS Kolloquium im Wintersemester 2014/15

Colloid crystallisation in a phase field crystal model - localised states and front motion

Prof. Dr. U. Thiele, Institut für Theoretische Physik

Im Rahmen des Kolloquiums der Materialphysik in Raum MP 619 in der IG 1

We discuss the modelling of aspects of colloidal crystallisation with two types of continuum models, namely, dynamical density functional theory (DDFT) and its local approximation, the phase field crystal (PFC) model [aka conserved Swift-Hohenberg (cSH) equation].

After introducing the field and the overall modelling approach, we first consider the structure of localised solutions of the PFC model that provides the simplest microscopic continuum description of the thermodynamic transition from a fluid state to a crystalline state and is frequently used to model colloidal crystallisation [1]. In particular, we analyse steady states and their bifurcations thereby focussing on the variety of spatially localized structures, that is found in addition to periodic structures [2]. The location of these structures in the temperature versus concentration plane is determined using a combination of numerical continuation in one dimension and direct numerical simulation in two and three dimensions. Localized states are found in the region of thermodynamic coexistence between the homogeneous and structured phases, and may lie outside of the binodal for these states. The relation of the existence of localised states and an amorphous solid phase is discussed.

Second, we analyse crystallisation fronts as described by the PFC model [3] and as well a full DDFT for soft particles [4]. We show that in the case of the PFC equation in 1d front speeds may be obtained via a marginal stability criterion [3]. The full 2d picture within the DDFT is more involved as there one needs to distinguish between linearly driven pulled fronts and nonlinearly driven pushed fronts as shown for the DDFT [4]. The relation of quench depth, front speed, created disorder and subsequent aging is discussed.

In the final part an outlook is given towards similar studies for binary colloidal mixtures that show stronger aging effects [4,5].

[1] H. Emmerich, H. Lowen, R. Wittkowski, T. Gruhn,
G. Toth, G. Tegze, and L. Granasy, Adv. Phys. 61, 665 (2012).
[2] U. Thiele, A. J. Archer, M. J. Robbins, H. Gomez, and E. Knobloch,
Phys. Rev. E. 87, 042915 (2013).
[3] A. J. Archer, M. J. Robbins, U. Thiele, and E. Knobloch,
Phys. Rev. E 86, 031603 (2012).
[4] A.J. Archer, M.C. Walters, U. Thiele, and E. Knobloch,
Phys. Rev. E , at press (2014).
[5] M. J. Robbins, A. J. Archer, U. Thiele, and E. Knobloch,
Phys. Rev. E 85, 061408 (2012).

Instabilities and singularities in problems involving phase change

Dr. Pierre Colinet, University Libre de Bruxelles
Einladender: U. Thiele

Phase change phenomena such as evaporation or solidification can lead to several types of instabilities, and may even trigger (or prevent) the formation of apparent singularities. In this talk, three topics will be considered: i) the surface-tension-driven instability of a thin liquid film evaporating into ambient atmosphere, for which the resulting polygonal pattern dynamics is examined both experimentally and theoretically; ii) the relaxation of viscous and thermal contact line singularities by evaporation/condensation processes, and the origin of evaporation-induced contact angles; iii) the formation of a cusp-like
singularity at the final stage of the freezing of a water drop on a cold substrate, for which experiments and theory allow highlighting a universal behavior as far as the selection of the final cusp (cone) angle is concerned.

Coarse-grained simulation of nanoparticle-protein interactions

Dr. Hender Lopez . School of Physics, University College Dublin
Einladender: U. Thiele

Gemeinsames Kolloquium mit dem CMTC

When nanoparticles (NP) enter a living organism, they are first  exposed to biological fluids, which leads to formation of a protein layer (protein corona) around the NP. It has been proposed that the composition and dynamics of the NP-protein corona determines its biological reactivity and toxicity [1]. Understanding the molecular mechanisms that lead to formation of the NP-protein corona is of capital importance and will certainly help to design NPs with specific functions for nanomedicine and to predict the toxicity of engineered nanoscale materials.

In the first part of the seminar we will review our recent work on a general Coarse-Grained (CG) model developed to calculate the adsorption energies of proteins onto hydrophobic NPs of arbitrary size. In this presentation, we give a detailed description of our model and numerical results on adsorption of six most abundant human blood plasma proteins on NPs of different radii and charge. Our results allow us to quantify the influence of NP surface curvature and charge on the adsorption energies. Our results for the adsorption energies and preferred globule orientations agree with previous full atomistic simulations [2]. We also present qualitative predictions for the composition of the NP-protein corona that agreed with experimental results [3].

In the second part of the talk we will present a CG model to describe the kinetics of adsorption of blood plasma proteins onto NPs. In contrast to previous works [4], our model includes the effect of hydrodynamics interactions on the formation of the NP-protein corona.

[1] Monopoli et al., Nature Nanotechnology 7 779 (2012)
[2] Brancolini et al., ACS Nano 6 9863 (2012). Ding et al., Nanoscale,
5 9162 (2013). Khan et al., J. Phys. Chem. Lett. 4 3747 (2013).
[3] De Paoli et al., ACS Nano 4 365 (2010).
[4] Vilaseca et al., Soft Matter 9 6978 (2013).

Data-driven inference of epileptic brain networks

Prof. Dr. Klaus Lehnertz, Neurophysics Group, Dept. of Epileptology, Medical Center University of Bonn
Einladender: O. Kamps

Complex networks are powerful representations of spatially extended systems and can advance our understanding of their dynamics. A large number of analysis techniques is now available that aim at inferring the underlying network from multivariate recordings of system observables. Despite great successes in various scientific fields, there still exist a number of problems, both conceptual and methodological, for which there are currently no satisfactory solutions. At the example of large-scale epileptic brain networks, I will present how the network approach can advance our understanding of the complex disease epilepsy and will discuss current shortcomings as well as possible research directions that may help to find better solutions.

From Markov State models to transition based equilibrium estimators:  a systematic approach to analyse molecular dynamics simulations

Dr.  Antonia Mey, Freie Universität Berlin, Computational Molecular Biology Group
Einladender: A. Heuer

Extracting quantitative equilibrium and dynamic estimates from molecular simulations, in particular with the interest of comparing these to experimental observables, is the aim of most simulators. However, this is often not a trivial task due to the complexity of the system and the timescales at which interesting processes occur. Markov state models (MSM) are a tool that allow to address these goals, by giving not only quantitative results for the equilibrium population of a molecular system, but can also be used to determine the dominant (slowest) processes (e.g. internal rearrangement of side chains of a protein) occurring in the system of interest. MSMs can even resolve timescales that are much longer than the individual trajectories used for the analysis, therefore trying to close the timescale gap which often plagues molecular simulations.
First, I will give a non-expert introduction to Markov state models and show how these can be readily constructed. As an illustrative example, I will show recent work of using MSMs to compare the influence of the choice of empirical molecular forcefield on the underlying dynamics of a few model peptides and highlight their differences.
Secondly, I will show how ideas from MSMs can be used to vastly improve stationary population estimates from multi-ensemble simulations (such as umbrella sampling or parallel tempering) by introducing a novel class of equilibrium estimators; the transition based analysis method (TRAM) estimators. TRAM estimators are asymptotically correct and reduce to estimation methods such as the weighted histogram analysis method (WHAM) and the multistate Bennet acceptance ratio method (MBAR) as special cases.
I will demonstrate how TRAM can outperform the state-of-the-art MBAR estimator by up to an order of magnitude, with respect to the total data used for analysis, on a selection of example systems of varying complexity.

References:
1. Speed of forcefields, J. Chem. Phys., under review
2. arXiv:1407.0138v1 Accepted for publication Phys. Rev. X

An Interfacial growth model for actin filament networks with a mechano-chemical coupling

Dr. Karin John, UJF Grenoble
Einladender: U. Thiele (zusammen mit dem TRR61 Münster-Beijing)

Many processes in eukaryotic cells, including cell motility, rely on the growth of branched actin filament networks from surfaces. Despite its central role, the mechano-chemical coupling mechanisms which guide the growth process in the presence of mechanical pre-stresses are poorly understood, and a general continuum description combining growth and mechanics is lacking.

We develop a theory based on discrete homogenization techniques, that bridges the gap between mesoscale and continuum limit and propose a general framework, that provides the evolution law of actin networks growing under stress. This formulation opens an area for the systematic study of actin dynamics in arbitrary geometries. Our framework predicts a morphological instability of actin growth on a rigid sphere, leading to a spontaneous polarization of the network with a mode selection corresponding to a comet, as reported experimentally. We show that the mechanics of the contact between the network and the surface plays a crucial role, in that it determines directly the existence of the instability. We extract scaling laws relating growth dynamics and network properties offering basic perspectives for new experiments on growing actin networks.

Optimal Control of Static Elastoplasticity with Hardening

Prof. Dr. Christian Meyer,  Technische Universität Dortmund
Einladender: B. Wirth

We consider an optimal control problem governed by a variational inequality (VI) of the first kind, which arises from a time discretization of a quasi-static model of elastoplastic deformation processes. The model is restricted to small strains and includes hardening of the material in form of linear kinematic hardening with the von Mises yield condition. After a short discussion of the VI and its reformulation in terms of a complementarity system, we focus on the derivation of necessary and sufficient optimality conditions. A severe issue in this context is the lack of regularity of the solution mapping associated with the VI, which is in general not Gateaux-differentiable. We present two different ways to circumvent this issue, a regularization approach and another technique which employs the directional derivative of the solution operator. While the latter one also allows to derive second-order sufficient optimality conditions, the regularization approach leads to an efficient optimization algorithm which allows to solve the problem numerically. The talk ends with the presentation of some numerical results.

Localised structures in nonlocal neural field models

Daniele Avitabile, School of Mathematical Sciences, University of Nottingham
Einladender: U. Thiele

I will discuss the formation of stationary localised solutions in 1D and 2D integral neural field models. First, a 1D inhomogeneous synaptic kernel with Heaviside firing rate will be considered. In this case, interface methods allow for the explicit construction of a bifurcation equation for localised steady states, so that analytical expressions for snakes and ladders can be derived. Similarly, eigenvalue computations can be carried out analytically to determine the stability of the solution profiles. I will then discuss a 2D model with homogeneous synaptic kernel that does not admit an equivalent PDE formulation. In this (and other neural field models featuring a convolution structure) it is advantageous to combine FFT and Newton-Krylov solvers to perform numerical bifurcation analysis directly on the integral model. I will present numerical results that show how the choice of synaptic kernel affects the bifurcation structure.

Sparse optimization of PDEs with application to light source placement in FDOT

Prof. Dr. Christian Clason, Fakultät für Mathematik Universität Duisburg-Essen
Einladender: B. Wirth

The problem of optimal placement of point sources such as optodes can be formulated as a distributed optimal control problem with sparsity constraints. Although well-posedness of this non-differentiable optimization problem requires a measure space setting, a conforming discretization of the space of Radon measures allows deriving primal-dual optimality conditions that conserve the relevant structural properties of the measure space problem and are amenable to solution by semismooth Newton methods.

Nonlinear stochastic differential equations: models, analysis and approximations

Prof. Dr. Arnulf Jentzen, ETH Zürich
Einladender: S. Dereich

This talk reviews recent developments in the regularity analysis and the numerical approximation of nonlinear stochastic differential equations (SDEs) and their associated deterministic second-order linear Kolmogorov partial differential equations (PDEs). Nonlinear SDEs appear, for example, in fundamental models from financial engineering, neurobiology and quantum field theory. In particular, we outline in this talk how nonlinear SEEs are day after day used in the financial engineering industry to estimate prices of financial derivatives. The nonlinearities in the SDEs from applications often fail to be globally Lipschitz continuous. A key topic of this talk is therefore the regularity analysis and the numerical approximation of SDEs with non-globally Lipschitz continuous nonlinearities.