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Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
Ensuring the safe and reliable operation of integrated electricity and gas systems (IEGS) requires dynamic energy flow (DEF) simulation tools that achieve high accuracy and computational efficiency. However, the inherent strong nonlinearity…
A new integration technique is presented for systems of linear partial differential equations (PDEs) for which syzygies can be formulated that obey conservation laws. These syzygies come for free as a by-product of the differential Groebner…
Modern modeling languages for general physical systems, such as Modelica, Amesim, or Simscape, rely on Differential Algebraic Equations (DAE), i.e., constraints of the form f(dot{x},x,u)=0. This drastically facilitates modeling from first…
Combustion stabilization and enhancement of the flammability limits are mandatory objectives to improve nowadays combustion chambers. At this purpose, the use of an electric field in the flame region provides a solution which is, at the…
We present a nonlinear dynamical model for DNA thermal denaturation, which is based on the finite stacking enthalpies used in thermodynamical nearest-neighbour calculations. Within this model, the finiteness of stacking enthalpies is shown…
The CALICE collaboration is developing calorimeters for a future linear collider, and has collected a large amount of physics data during test beam efforts. For the analysis of these data, standard software available for linear collider…
We present a novel thermodynamically guided, low-noise, time-scale bridging, and pertinently efficient strategy for the dynamic simulation of microscopic models for complex fluids. The systematic coarse-graining method is exemplified for…
We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions.…
Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and…
Many coarse-grained models have been developed for equilibrium studies of lipid bilayer membranes. To achieve in simulations access to length-scales and time-scales difficult to attain in fully atomistic molecular dynamics, these…
A new approach to simulating warm and hot dense matter that combines density functional theory based calculations of the electronic structure to classical molecular dynamics simulations with pair interaction potentials is presented. The new…
In radio frequency applications, electric circuits generate signals, which are amplitude modulated and/or frequency modulated. A mathematical modelling yields typically systems of differential algebraic equations (DAEs). A multivariate…
We present a multi-model simulation approach, targeted at understanding the behavior of comminution and the effect of grinding aids (GAs) in industrial cement mills. On the atomistic scale we use Molecular Dynamics (MD) simulations with…
Challenging stellar dynamical problems, such as the study of gravothermal oscillations in star clusters, have in the past initiated the very successful building of GRAPE special purpose computers. It is discussed, that present day tasks…
We construct a coarse-grained (CG) model for dipalmitoylphosphatidylcholine (DPPC)/cholesterol bilayers and apply it to large-scale simulation studies of lipid membranes. Our CG model is a two-dimensional representation of the membrane,…
Carleman linearization is a mathematical technique that transforms nonlinear dynamical systems into infinite-dimensional linear systems, enabling simplified analysis. Initially developed for ordinary differential equations (ODEs) and later…
We present a multiscale hybrid particle-field scheme for the simulation of relaxation and diffusion behavior of soft condensed matter systems. It combines particle-based Brownian dynamics and field-based local dynamics in an adaptive sense…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…