Convergence of a linearly transformed particle method for aggregation equations

We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in $L^1$ and $L^\infty$ norms depending on the regularity of the initial data. Moreover, we give convergence estimates in bounded Lipschitz distance for measure valued solutions. For singular interaction forces, we establish the convergence of the error between the approximated and exact flows up to the existence time of the solutions in $L^1 \cap L^p$ norm

Physics-based visual characterization of molecular interaction forces

Molecular simulations are used in many areas of biotechnology, such as drug design and enzyme engineering. Despite the development of automatic computational protocols, analysis of molecular interactions is still a major aspect where human comprehension and intuition are key to accelerate, analyze, and propose modifications to the molecule of interest. Most visualization algorithms help the users by providing an accurate depiction of the spatial arrangement: the atoms involved in inter-molecular contacts. There are few tools that provide visual information on the forces governing molecular docking. However, these tools, commonly restricted to close interaction between atoms, do not consider whole simulation paths, long-range distances and, importantly, do not provide visual cues for a quick and intuitive comprehension of the energy functions (modeling intermolecular interactions) involved. In this paper, we propose visualizations designed to enable the characterization of interaction forces by taking into account several relevant variables such as molecule-ligand distance and the energy function, which is essential to understand binding affinities. We put emphasis on mapping molecular docking paths obtained from Molecular Dynamics or Monte Carlo simulations, and provide time-dependent visualizations for different energy components and particle resolutions: atoms, groups or residues. The presented visualizations have the potential to support domain experts in a more efficient drug or enzyme design process.Peer ReviewedPostprint (author's final draft

Contacts With Negative Work of “Adhesion” and Superlubricity

Van der Waals forces between solids in vacuum are always attractive and are considered as the main source of adhesion. However, in the presence of an intermediate medium, they can also be repelling (Dzyaloshinskii et al., 1961) which means that the “work of adhesion” becomes negative. Similarly to the case of adhesion, the interaction range of these forces can be either comparable (or larger) than the minimum characteristic length scale of the contact problem or it can be negligible compared with all characteristic length scales. We call this latter case the “JKR-approximation,” as the JKR theory of adhesion (Johnson et al., 1971) is also valid in this limit. The repelling interaction can also be due to the presence (and squeezing out) of a thin fluid layer between solids as considered in Müser (2014). In the papers Popov and Hess (2018) and Heß and Popov (2019), it was shown that the contact of two oppositely charged surfaces at a constant voltage is equivalent to the adhesive contact with an effective van der Waals interaction. Similarly, the contact of the bodies with the same charge would be equivalent to repelling van der Waals forces with a negative work of adhesion. Further kinds of repelling forces may be solvation, structural, and hydration forces (Israelachvili, 2011). In the following, we speak about van der Waals forces, but they are thought as representative for a larger class of long range repelling forces. We argue that in the JKR approximation, the Hertz' solution of the contact problem with a repelling van der Waals interaction, remains practically unchanged. However, the contact area falls apart into the area of “weak (van der Waals) interaction” and “strong (rigid wall) interaction.” It is speculated that if the normal force is smaller than a critical value at which the core region of strong interaction disappears, a macroscopic superlubricity state of the contact may be observed.DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli

Salt-induced changes of colloidal interactions in critical mixtures

We report on salt-dependent interaction potentials of a single charged particle suspended in a binary liquid mixture above a charged wall. For symmetric boundary conditions (BC) we observe attractive particle-wall interaction forces which are similar to critical Casimir forces previously observed in salt-free mixtures. However, in case of antisymmetric BC we find a temperature-dependent crossover from attractive to repulsive forces which is in strong contrast to salt-free conditions. Additionally performed small-angle x-ray scattering experiments demonstrate that the bulk critical fluctuations are not affected by the addition of salt. This suggests that the observed crossover can not be attributed alone to critical Casimir forces. Instead our experiments point towards a possible coupling between the ionic distributions and the concentration profiles in the binary mixture which then affects the interaction potentials in such systems.Comment: 5 pages, 4 Figure

The Röntgen interaction and forces on dipoles in time-modulated optical fields

The Röntgen term is an often neglected contribution to the interaction between an atom and an electromagnetic field in the electric dipole approximation. In this work we discuss how this interaction term leads to a difference between the kinetic and canonical momentum of an atom which, in turn, leads to surprising radiation forces acting on the atom. We use a number of examples to explore the main features of this interaction, namely forces acting against the expected dipole force or accelerations perpendicular to the beam propagation axis