Tanja Schilling
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View article: On the generalized Langevin equation and the Mori projection operator technique
On the generalized Langevin equation and the Mori projection operator technique Open
In statistical physics, the Nakajima-Mori-Zwanzig projection operator formalism is used to derive an integro-differential equation for observables in a Hilbert space, the generalized Langevin equation (GLE). This technique relies on the sp…
View article: Evolution equations for open systems and collective variables: Which equation would you like to solve by molecular dynamics simulation?
Evolution equations for open systems and collective variables: Which equation would you like to solve by molecular dynamics simulation? Open
In molecular dynamics simulations, the Langevin equation is frequently used to model the dynamics of collective variables and of systems coupled to baths. Often, external forces are added to the Langevin equation (e.g., when using targeted…
View article: Structural transition in the single layer growth of diindenoperylene on silica
Structural transition in the single layer growth of diindenoperylene on silica Open
When forming a film on a substrate, rod shaped organic molecules can order in lying-down or standing-up phases. We have studied the growth of diindenoperylene films on amorphous silicon dioxide by means of molecular dynamics simulations an…
View article: Polydispersity in Percolation
Polydispersity in Percolation Open
Every realistic instance of a percolation problem is faced with some degree of polydispersity, e.g., the pore-size distribution of an inhomogeneous medium, the size distribution of filler particles in composite materials, or the vertex deg…
View article: Flow-induced anisotropy in a carbon black-filled silicone elastomer: electromechanical properties and structure
Flow-induced anisotropy in a carbon black-filled silicone elastomer: electromechanical properties and structure Open
Carbon black (CB)-elastomers can serve as low-cost, highly deformable sensor materials, but hardly any work exists on their structure-property relationships. We report on flow-induced anisotropy, considering CB-silicone films generated via…
View article: Analysis of the Dynamics in Linear Chain Models by means of Generalized Langevin Equations
Analysis of the Dynamics in Linear Chain Models by means of Generalized Langevin Equations Open
We analyse the motion of one particle in a polymer chain. For this purpose, we use the framework of the exact (non-stationary) generalized Langevin equation that can be derived from first principles via the projection-operator method. Our …
View article: Tracer dynamics in polymer networks: Generalized Langevin description
Tracer dynamics in polymer networks: Generalized Langevin description Open
Tracer diffusion in polymer networks and hydrogels is relevant in biology and technology, while it also constitutes an interesting model process for the dynamics of molecules in fluctuating, heterogeneous soft matter. Here, we systematical…
View article: Work, Heat and Internal Energy in Open Quantum Systems: A Comparison of Four Approaches from the Autonomous System Framework
Work, Heat and Internal Energy in Open Quantum Systems: A Comparison of Four Approaches from the Autonomous System Framework Open
We compare definitions of the internal energy of an open quantum system and strategies to split the internal energy into work and heat contributions as given by four different approaches from the autonomous system framework. Our discussion…
View article: Nonequilibrium solvent response force: What happens if you push a Brownian particle
Nonequilibrium solvent response force: What happens if you push a Brownian particle Open
In this Letter we discuss how to add forces to the Langevin equation. We derive an exact generalized Langevin equation for the dynamics of one particle subject to an external force embedded in a system of many interacting particles. The ex…
View article: Tracer dynamics in polymer networks: generalized Langevin description
Tracer dynamics in polymer networks: generalized Langevin description Open
Tracer diffusion in polymer networks and hydrogels is relevant in biology and technology, while it also constitutes an interesting model process for the dynamics of molecules in fluctuating, heterogeneous soft matter. Here, we study system…
View article: The non-equilibrium solvent response force: What happens if you push a Brownian particle
The non-equilibrium solvent response force: What happens if you push a Brownian particle Open
In this letter we discuss how to add forces to the Langevin equation. We derive the exact generalized Langevin equation for the dynamics of one particle subject to an external force embedded in a system of many interacting particles. The e…
View article: A universally applicable approach to connectivity percolation
A universally applicable approach to connectivity percolation Open
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold. Unl…
View article: Work, Heat and Internal Energy in Open Quantum Systems: A Comparison of Four Approaches from the Autonomous System Framework
Work, Heat and Internal Energy in Open Quantum Systems: A Comparison of Four Approaches from the Autonomous System Framework Open
We compare definitions of the internal energy of an open quantum system and strategies to split the internal energy into work and heat contributions as given by four different approaches from autonomous system framework. Our discussion foc…
View article: Optimizing the structure of acene clusters
Optimizing the structure of acene clusters Open
We present a study of the potential energy surface of anthracene, tetracene, and pentacene clusters with up to 30 molecules. We have applied the basin-hopping Monte Carlo algorithm to clusters of acene molecules in order to find their lowe…
View article: Generalized Langevin dynamics simulation with non-stationary memory kernels: How to make noise
Generalized Langevin dynamics simulation with non-stationary memory kernels: How to make noise Open
We present a numerical method to produce stochastic dynamics according to the generalized Langevin equation with a non-stationary memory kernel. This type of dynamics occurs when a microscopic system with an explicitly time-dependent Liouv…
View article: Generalized Langevin dynamics simulation with non-stationary memory kernels: How to make noise
Generalized Langevin dynamics simulation with non-stationary memory kernels: How to make noise Open
We present a numerical method to produce stochastic dynamics according to the generalized Langevin equation with a non-stationary memory kernel. This type of dynamics occurs when a microscopic system with an explicitly time-dependent Liouv…
View article: Hard Sphere Crystal Nucleation Rates: Reconciliation of Simulation and Experiment
Hard Sphere Crystal Nucleation Rates: Reconciliation of Simulation and Experiment Open
Over the past two decades, a large number of studies addressed the topic of crystal nucleation in suspensions of hard spheres. The shared result of all these efforts is that, at low supersaturations, experimentally observed nucleation rate…
View article: Excluded volume interactions and phase stability in mixtures of hard spheres and hard rods
Excluded volume interactions and phase stability in mixtures of hard spheres and hard rods Open
Phase behaviour of binary rod/sphere mixtures: Verification of a novel free volume theory approach with Monte Carlo simulations.
View article: The interplay between memory and potentials of mean force: A discussion on the structure of equations of motion for coarse-grained observables
The interplay between memory and potentials of mean force: A discussion on the structure of equations of motion for coarse-grained observables Open
The underdamped, non-linear, generalized Langevin equation is widely used to model coarse-grained dynamics of soft and biological materials. By means of a projection operator formalism, we show under which approximations this equation can …
View article: Percolation of rigid fractal carbon black aggregates
Percolation of rigid fractal carbon black aggregates Open
We examine network formation and percolation of carbon black by means of Monte Carlo simulations and experiments. In the simulation, we model carbon black by rigid aggregates of impenetrable spheres, which we obtain by diffusion-limited ag…
View article: Generating functions for message-passing on weighted networks: directed bond percolation and SIR epidemics
Generating functions for message-passing on weighted networks: directed bond percolation and SIR epidemics Open
We study the SIR ("susceptible, infected, removed/recovered") model on directed graphs with heterogeneous transmission probabilities within the message-passing approximation. We characterize the percolation transition, predict cluster size…
View article: The Interplay between Memory and Potentials of Mean Force: A Discussion on the Structure of Equations of Motion for Coarse Grained Observables
The Interplay between Memory and Potentials of Mean Force: A Discussion on the Structure of Equations of Motion for Coarse Grained Observables Open
The underdamped, non-linear, generalized Langevin equation is widely used to model coarse-grained dynamics of soft and biological materials. By means of a projection operator formalism, we show under which approximations this equation can …
View article: Comments on the validity of the non-stationary generalized Langevin equation as a coarse-grained evolution equation for microscopic stochastic dynamics
Comments on the validity of the non-stationary generalized Langevin equation as a coarse-grained evolution equation for microscopic stochastic dynamics Open
We recently showed that the dynamics of coarse-grained observables in systems out of thermal equilibrium are governed by the non-stationary generalized Langevin equation [H. Meyer, T. Voigtmann, and T. Schilling, J. Chem. Phys. 147, 214110…
View article: Nearest-neighbor connectedness theory: A general approach to continuum percolation
Nearest-neighbor connectedness theory: A general approach to continuum percolation Open
We introduce a method to estimate continuum percolation thresholds and illustrate its usefulness by investigating geometric percolation of noninteracting line segments and disks in two spatial dimensions. These examples serve as models for…
View article: Evaluation of memory effects at phase transitions and during relaxation processes
Evaluation of memory effects at phase transitions and during relaxation processes Open
We propose to describe the dynamics of phase transitions in terms of a nonstationary generalized Langevin equation for the order parameter. By construction, this equation is nonlocal in time, i.e., it involves memory effects whose intensit…
View article: A Numerical Procedure to Evaluate Memory Effects in Non‐Equilibrium Coarse‐Grained Models
A Numerical Procedure to Evaluate Memory Effects in Non‐Equilibrium Coarse‐Grained Models Open
When developing coarse‐grained models of complex processes out of equilibrium, one encounters the non‐stationary generalized Langevin equation. The most important feature of this equation is the presence of a non‐stationary memory kernel. …
View article: Computation of the solid-liquid interfacial free energy in hard spheres by means of thermodynamic integration
Computation of the solid-liquid interfacial free energy in hard spheres by means of thermodynamic integration Open
We used a thermodynamic integration scheme, which is specifically designed for disordered systems, to compute the interfacial free energy of the solid-liquid interface in the hard-sphere model. We separated the bulk contribution to the tot…