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Mobility is an indispensable part of modern human societies, but the dominance of motorized individual traffic (MIV, i.e., the private car) leads to a prohibitive waste of energy as well as other resources. Here we show that by combining a line service (e.g., railway) system with a fleet of ride-pooling shuttles connecting line stops to desired pick-up and drop-off points, a bi-modal public transport system may result which provides on-demand door-to-door service at a service level (in terms of transit times) superior to current public transport, and with an overall comfort level comparable to MIV. We identify the conflicting objectives for optimization, i.e., user convenience and energy consumption, and evaluate the system performance in terms of Pareto fronts. By means of simulation and analytical theory, we find that energy consumption can be as low as 20% of MIV, at line service densities typically found in real settings. Surprisingly, we find favorable performance not only in urban, but also in rural settings., Comment: 18 pages, 8 figures, 1 table

The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture bulk real-world 3D protein-protein properties well. One approach is using protein contact maps to better understand proteins' properties. Here, we investigate the emergent behaviour of contact maps for different geometrically constrained models and real-world protein systems. We derive an analytical approximation for the distribution of model amino acid distances, $s$, by means of a mean-field approach. This approximation is then validated for simulations using a 2D and 3D random interaction model, as well as from contact maps of real-world protein data. Using data from the RCSB Protein Data Bank (PDB) and AlphaFold~2 database, the analytical approximation is fitted to protein chain lengths of $L\approx100$, $L\approx200$, and $L\approx300$. While a universal scaling behaviour for protein chains of different lengths could not be deduced, we present evidence that the amino acid distance distributions can be attributed to geometric constraints of protein chains in bulk and amino acid sequences only play a secondary role., Comment: 15 pages, 4 figures

The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino acids, the biochemical environment and the temporal sequence of distinct interactions yield a complex folding process that cannot yet be easily tracked for all proteins. To gain qualitative insights into the fundamental mechanisms behind the folding dynamics and generic features of the folded structure, we propose a simple model of structure formation that takes into account only fundamental geometric constraints and otherwise assumes randomly paired connections. We find that despite its simplicity, the model results in a network ensemble consistent with key overall features of the ensemble of Protein Residue Networks we obtained from more than 1000 biological protein geometries as available through the Protein Data Base. Specifically, the distribution of the number of interaction neighbors a unit (amino acid) has, the scaling of the structure's spatial extent with chain length, the eigenvalue spectrum and the scaling of the smallest relaxation time with chain length are all consistent between model and real proteins. These results indicate that geometric constraints alone may already account for a number of generic features of protein tertiary structures.

Generation of electromagnetic fields by moving charges is a fascinating topic where the tight connection between classical electrodynamics and special relativity becomes particularly apparent. One can gain direct insight into the fascinating structure of such fields by visualizing the electric field lines. However, the calculation of electric field lines for arbitrarily moving charges is far from trivial. Here, we derive an equation for the director that points from the retarded position of a moving charge towards a specific field line position, which allows for a simple construction of these lines. We analytically solve this equation for several special but important cases: for an arbitrary rectilinear motion, for the motion within the wiggler magnetic field of a free electron laser, and for the motion in a synchrotron., Comment: 6 pages, 7 figures

When comet nuclei approach the Sun, the increasing energy flux through the surface layers leads to sublimation of the underlying ices and subsequent outgassing that promotes the observed emission of gas and dust. The ejection of dust requires that the forces binding the dust particles to the comet nucleus must be overcome by the forces caused by the sublimation process. This relates to the question of how large the tensile strength of the overlying dust layer is. Homogeneous layers of micrometer-sized dust particles reach tensile strengths of typically $10^3$ to $10^4$ Pa. This exceeds by far the maximum sublimation pressure of water ice in comets. It is therefore unclear how cometary dust activity is driven. To solve this paradox, we used the model by Skorov and Blum (Icarus 221, 1-11, 2012), who assumed that cometesimals formed by gravitational instability of a cloud of dust and ice aggregates and calculated for the corresponding structure of comet nuclei tensile strength of the dust-aggregate layers on the order of 1 Pa. Here we present evidence that the emitted cometary dust particles are indeed aggregates with the right properties to fit the model by Skorov and Blum. Then we experimentally measure the tensile strengths of layers of laboratory dust aggregates and confirm the values derived by the model. To explain the comet activity driven by the evaporation of water ice, we derive a minimum size for the dust aggregates of $\sim 1$ mm, in agreement with meteoroid observations and dust-agglomeration models in the solar nebula. Finally we conclude that cometesimals must have formed by gravitational instability, because all alternative formation models lead to higher tensile strengths of the surface layers., Comment: The pdf file includes the main document and the corrigendum to the main article (just scroll through the pdf)