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All entomological traps have a capturing bias, and amber, viewed as a trap, is no exception. Thus the fauna trapped in amber does not represent the total existing fauna of the former amber forest, rather the fauna living in and around the resin producing tree. In this paper we compare arthropods from a forest very similar to the reconstruction of the Miocene Mexican amber forest, and determine the bias of different trapping methods, including amber. We also show, using cluster analyses, measurements of the trapped arthropods, and guild distribution, that the amber trap is a complex entomological trap not comparable with a single artificial trap. At the order level, the most similar trap to amber is the sticky trap. However, in the case of Diptera, at the family level, the Malaise trap is also very similar to amber. Amber captured a higher diversity of arthropods than each of the artificial traps, based on our study of Mexican amber from the Middle Miocene, a time of climate optimum, where temperature and humidity were probably higher than in modern Central America. We conclude that the size bias is qualitatively independent of the kind of trap for non-extreme values. We suggest that frequent specimens in amber were not necessarily the most frequent arthropods in the former amber forest. Selected taxa with higher numbers of specimens appear in amber because of their ecology and behavior, usually closely related with a tree-inhabiting life. Finally, changes of diversity from the Middle Miocene to Recent time in Central and South America can be analyzed by comparing the rich amber faunas from Mexico and the Dominican Republic with the fauna trapped using sticky and Malaise traps in Central America.

The statistics of how the local environment of a particle looks like, e.g., given by the distribution of nearest neighbor distances or the sizes of Voronoi cells, is important as a starting point for the calculation of many material properties like electronic or photonic band structures. Here we study local environments that occur in quasicrystals with large rotational symmetry. Both with analytical considerations based on geometric arguments and with an analysis of a large number of numerically created patches of high-symmetry quasicrystals we find that the Voronoi area’s distribution reaches a bimodal curve and that in the limit of large rotational symmetries the distribution of nearest neighbor distance converges against a universal curve, where 27.7 % of the vertices have their nearest neighbor at a normalized distance equal to 1, while for the other 72.3 % the nearest neighbor is at a distance less than 1. Therefore, the statistics of local environments is non-trivial but independent of the specific rotational symmetry. Thus properties that only depend on local environments are expected to be universal for all high-symmetry quasicrystals.

Background The genera Agathis (Coniferales: Araucariaceae) and Hymenaea (Fabales: Fabaceae) contain resin-producing tree species that are crucial for actuotaphonomic studies. While certain Cretaceous ambers likely originated from Agathis or Agathis -like trees, Hymenaea is the primary source of many Miocene ambers. Field studies were conducted in New Caledonia and Madagascar to collect Defaunation resin (resin produced after 1760 AD (Anno Domini)). Arthropods were collected with yellow sticky and Malaise traps in New Caledonia, Madagascar, and Mexico. Cretaceous and Miocene ambers, copals (2.58 Ma to 1760 AD), and Defaunation resins from various regions were analysed to compare arthropod trapping patterns. Results Actuotaphonomic results show lower number of arthropods trapped in Agathis Defaunation resin, with a non-uniform distribution, compared to the abundant and uniformly distributed arthropods trapped in Hymenaea Defaunation resin. The lower number of arthropod inclusions in the trunk resin of the Agathis trees is attributed to the rapid polymerisation of that resin. Under the same experimental conditions, the arthropods in Agathis Defaunation resin plot far from the arthropods collected in the yellow sticky and Malaise traps, while the arthropods in Hymenaea Defaunation resin plot close to the arthropods in the yellow sticky traps. Conclusions These findings confirm different resin trapping patterns between Agathis and Hymenaea , with significant implications for interpreting the amber record. The fauna trapped by Hymenaea resin closely resembles the arthropod biocoenosis that live in and around the trunks, indicating autochthony and close relationship with the forest ecosystem, unlike Agathis resin. These results improve our understanding of arthropod trapping biases in resin and lead us to reconsider previously proposed interpretations of Cretaceous forest biocoenoses.

We introduce an algorithm based on Generalized Dual Method (GDM) to efficiently study the dynamics of a particle in quasiperiodic environments without the need to use periodic approximations or to save the information of the vertices that make up the quasiperiodic lattice. We show that the computation time and the memory required to find the tile in which a particle is located as a function of the distance \\(R\\) to the center of symmetry remains constant in our algorithm, while using the GDM directly both quantities go like \\(R^2\\).This allows us to perform realistic simulations with low consumption of computational resources. The algorithm can be used to study any quasiperiodic lattice that can be produced by the cut-and-project method. Using this algorithm, we have calculated the free path length distribution in quasiperiodic Lorentz gases reproducing previous results and for systems with high symmetries at the Boltzmann-Grad limit. We have found for the Boltzmann-Grad limit, that the distribution of free paths depends on the rank \\(r\\) of the quasiperiodic system and not on its symmetry. The distribution as a function of the free path length \\(l\\) appears to be a combination of exponential decay and a power-law behavior. The latter seems to become important only for probabilities less than \\((2^{r-2} r (r+1))^{-1}\\), showing an exponential decaying free-path length distribution for \\(r \\rightarrow \\infty\\), similar to what is observed in disordered systems.

We introduce the concept of dynamic neighbors. This concept defines an order parameter with which phase transitions and jamming can be detected in fluids of hard-spheres without considering orientational or translational symmetry. It also gives a method to estimate the configurational entropy of the system. Using molecular dynamics simulations, we measure the number of dynamic neighbors. With this, it is possible to detect three phases in \\(2\\)-dimensional system and two phases in the \\(3\\)-dimensional version. In the hard disk system, these regions correspond to the fluid, hexatic and solid phases, while in the \\(3\\)-dimensional case, they correspond to the solid and fluid phase. We observe a continuous transition in the \\(2\\)-dimensional system and a first-order phase transition in the \\(3\\)-dimensional case. We also observe only two \"states\" in the case of binary mixtures and for hard-spheres with a fast compression speed. These two states correspond to fluid and jammed states.

We study a 2-dimensional model for an antidot periodic superlattice with perturbed positions of the antidots. To do so we use a quasiperiodic LG model obtained from a 3-dimensional billiard model. Our results show that infinite drifting trajectories present in the periodic antidot models disappear, but if the perturbation is small enough, those trajectories remain for long times. The probability to visit the region of the phase space where electrons have ballistic behavior tends to \\(0\\) as the length of the drifting trajectories tends to infinity, leading to separation of these regions in phase space. As a result, we infer that the particles follow Levy walks and the system has superdiffusive behavior for short times. The superdiffusive exponent is correlated to the length of time where the superdiffusive behavior is present.

We show, incorporating results obtained from numerical simulations, that in the Lorentz mirror model, the density of open paths in any finite box tends to 0 as the box size tends to infinity, for any mirror probability.

We study the structure of quasiperiodic Lorentz gases, i.e., particles bouncing elastically off fixed obstacles arranged in quasiperiodic lattices. By employing a construction to embed such structures into a higher dimensional periodic hyperlattice, we give a simple and efficient algorithm for numerical simulation of the dynamics of these systems. This same construction shows that quasiperiodic Lorentz gases generically exhibit a regime with infinite horizon, that is, empty channels through which the particles move without colliding, when the obstacles are small enough; in this case, the distribution of free paths is asymptotically a power law with exponent -3, as expected from infinite-horizon periodic Lorentz gases. For the critical radius at which these channels disappear, however, a new regime with locally-finite horizon arises, where this distribution has an unexpected exponent of -5, previously observed only in a Lorentz gas formed by superposing three incommensurable periodic lattices in the Boltzmann-Grad limit where the radius of the obstacles tends to zero.

We present efficient algorithms to calculate trajectories for periodic Lorentz gases consisting of square lattices of circular obstacles in two dimensions, and simple cubic lattices of spheres in three dimensions; these become increasingly efficient as the radius of the obstacles tends to 0, the so-called Boltzmann-Grad limit. The 2D algorithm applies continued fractions to obtain the exact disc with which a particle will collide at each step, instead of using periodic boundary conditions as in the classical algorithm. The 3D version incorporates the 2D algorithm by projecting to the three coordinate planes. As an application, we calculate distributions of free path lengths close to the Boltzmann-Grad limit for certain Lorentz gases. We also show how the algorithms may be applied to deal with general crystal lattices.

We introduce a construction to embed a quasiperiodic lattice of obstacles into a single unit cell of a higher-dimensional space, with periodic boundary conditions. This construction transparently shows the existence of channels in these systems,in which particles may travel without colliding, up to a critical obstacle radius. It provides a simple and efficient algorithm for numerical simulation of dynamics in quasiperiodic structures, as well as giving a natural notion of uniform distribution (measure) and averages. As an application, we simulate diffusion in a two-dimensional quasicrystal, finding three different regimes, in particular atypical weak super-diffusion in the presence of channels, and sub-diffusion when obstacles overlap.