GAMM2025

Session

S26: Modelling, Analysis and Simulation of Molecular Systems

S26

9 Apr 2025, 08:30

Lecture and Conference Centre

Conveners

S26: Modelling, Analysis and Simulation of Molecular Systems: S26.01

• Benjamin Stamm

S26: Modelling, Analysis and Simulation of Molecular Systems: S26.02

• Feliks Nüske

S26: Modelling, Analysis and Simulation of Molecular Systems: S26.03

• Sebastian Matera

759. The Quasi-Stationary Distribution approach to metastability

Tony Lelievre

09/04/2025, 08:30

We will discuss models used in classical molecular dynamics, and some mathematical questions raised by their simulations. In particular, we will present recent results on the connection between a metastable Markov process with values in a continuous state space (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process with values in a discrete state space. This...

389. On-the-fly adaptive sparse grids for coupling molecular monte-carlo and continuum models

Tobias Hülser

09/04/2025, 09:10

Most simulations of continuum models require the repetitive evaluation of some non-linear functions. If these functions are only implicitly given by the outcome of some expensive high-fidelity model, these evaluations can easily become the computational bottleneck of this coupled simulation. A surrogate model for the high-fidelity part is therefore needed. However, if the input dimension of...

390. Koopman-based Control for Stochastic Systems: Application to Enhanced Sampling

Lei Guo

09/04/2025, 09:30

Stochastic dynamics with metastability are a recurring theme in many scientific disciplines, for instance, in simulations of macro-molecules, in climate systems, and in applications of uncertainty quantification. Metastability describes the existence of long-lived macro-states in a dynamical system's state space, such that transitions between these macro-states are rare events. It is thus also...

391. Coarse-grained simulation of protein self-assembly

Lukas Mayrhofer

09/04/2025, 09:50

We present our work on simulating the self-assembly of large protein systems, with a focus on the assembly of tobacco mosaic virus coat proteins into a helical shell. The size and timescales of these systems make all-atom molecular dynamics simulations unfeasible.

To tackle this, we constrain the proteins to a single conformation and introduce a coarse-grained energy model that includes van...

774. Family of Gaussian wavepacket dynamics methods from the perspective of a nonlinear Schrödinger equation

Jiri Vanicek

09/04/2025, 16:30

Many approximate solutions of the time-dependent Schrödinger equation can be formulated as exact solutions of a nonlinear Schrödinger equation with an effective Hamiltonian operator depending on the state of the system. We show that Heller's thawed Gaussian approximation, Coalson and Karplus's variational Gaussian approximation, and other Gaussian wavepacket dynamics methods fit into this...

392. Multiresolution of the free-particle propagator

Evgueni Dinvay

09/04/2025, 17:10

This work focuses on numerical methods for simulating the time evolution of the Schrödinger equation, primarily in one dimension. Symplectic splitting algorithms are employed to separate the kinetic and potential components of the propagator. The semigroup associated with the free-particle Schrödinger operator is then represented in a multiwavelet basis. In the talk, I will demonstrate how to...

393. Second-Order Time-Splitting Hermite Spectral Method for Nonlinear Schrödinger Equations with Time-Dependent Potential

Paul Bergold

09/04/2025, 17:30

We present a novel numerical method for solving nonlinear Schrödinger (NLS) equations with time-dependent potentials on the real line. The spatial discretization employs a Hermite spectral decomposition, providing analytical expressions for the evolution of basis functions under the free Schrödinger operator. A linearization approach for solutions to the underlying NLS equation with...

394. Quasivoids in polydisperse glassy systems with atomistic PEL exploration and iso-configuration method

S. Swayamjyoti

09/04/2025, 17:50

Supercooled liquids exhibit spatial heterogeneity in the dynamics of their fluctuating atomic arrangements, with particle dynamics often dominated by stringlike motions where lines of particles perform activated hops cooperatively [1]. In glassy systems, a void takes the form of a quasivoid composed of a few neighboring free volumes and is transported through the stringlike motions it induces...

356. Analysis of an inexact domain decomposition method with application to the Conductor-like Screening model

Nibedita Ghosh

09/04/2025, 18:10

The conductor-like screening model or COSMO model is used for computing the electrostatic interaction between a solvent and a particular solute molecule. Mathematically this involves solving a Laplace boundary value problem on a domain with a large number of intersecting balls. We proposed to solve this problem more efficiently by employing a numerical method based on Schwarz's domain...

357. Wigner crystallization

Gero Friesecke

10/04/2025, 08:30

An accurate numerical method is presented for computing the ground state of a many-electron system in the low-density limit first considered by Seidl (Phys. Rev. A 1999). In this limit the ground state problem reduces to a multi-marginal optimal transport (MMOT) problem. The method is an improved version of the Genetic Column Generation algorithm by Friesecke, Schulz and Voegler introduced in...

358. A mathematical analysis of IPT-DMFT

Solal Perrin-Roussel

10/04/2025, 09:10

In this talk, I will present a mathematical analysis of Dynamical Mean-Field Theory (DMFT), a Green's function method developed in the 1990s, which provides dynamical correlations associated with the Gibbs state of fermionic quantum lattice models (e.g. the Hubbard model). In particular, I will show the existence of a solution to the corresponding equations in the framework of Iterated...

359. Certified Model Order Reduction for parametric Hermitian eigenproblems

Zhuoyao Zeng

10/04/2025, 09:30

We deal with efficient and certified numerical approximation of parametric Hermitian eigenproblems. For this aim, we rely on projection-based model order reduction, i.e. we approximate a possibly large-scale problem with one of a much smaller dimension by projecting it on a suitable subspace. Such a space is constructed by means of weak-greedy type strategies applied either on a continuum or...

360. Riemannian Optimisation Methods for Ground States of Multicomponent Bose-Einstein Condensates

Martin Hermann

10/04/2025, 09:50

This talk addresses the computation of ground states of multicomponent Bose-Einstein condensates, defined as the global minimizer of an energy functional on an infinite -dimensional generalized oblique manifold. We establish the existence of the ground state and characterize it as the solution to a coupled nonlinear eigenvector problem. By equipping the manifold with several Riemannian...

361. An Energy-Adaptive Riemannian Conjugate Gradient Method for Eigenvector Problems of Kohn-Sham Type

Jonas Püschel

10/04/2025, 10:10

Eigenvector problems of the Kohn-Sham type often arise in computational physics and chemistry and can be formulated as minimization of an energy functional on the Stiefel manifold. We propose to use the Hamiltonian operator of the system to construct a Riemannian metric on the Stiefel manifold. This allows us to formulate the energy-adaptive Riemannian conjugate gradient method. Numerical...