Related papers: Cosmic crystallography: the euclidean isometries
Many real objects are modeled as discrete sets of points, such as corners or other salient features. For our main applications in chemistry, points represent atomic centers in a molecule or a solid material. We study the problem of…
Constraining the physical and chemical evolution of molecular clouds is essential to our understanding of star formation. These investigations often necessitate knowledge of some local representative number density of the gas along the line…
Extended gas haloes around galaxies are a ubiquitous prediction of galaxy formation scenarios. However, the density profiles of this hot halo gas is virtually unknown, although various profiles have been suggested on theoretical grounds. In…
We derive an exact, simple relation between the average number of clusters and the wrapping probabilities for two-dimensional percolation. The relation holds for periodic lattices of any size. It generalizes a classical result of Sykes and…
We introduce a computational method to discover polymorphs in molecular crystals at finite temperature. The method is based on reproducing the crystallization process starting from the liquid and letting the system discover the relevant…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
Planets reflect and linearly polarize the radiation that they receive from their host stars. The emergent polarization is sensitive to aspects of the planet atmosphere such as the gas composition and the occurrence of condensates and their…
The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…
We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly…
The knowledge of the redshift of multiple images in cluster-lenses allows to determine precisely the total projected mass within the Einstein radius. The observation of various multiple images in a same cluster is opening new possibilities…
The ground state of a two-dimensional, harmonically confined mesoscopic assembly of up to thirty polar molecules is studied by computer simulations. As the strength of the confining trap is increased, clusters evolve from superfluid, to…
The decomposition of an image into a linear combination of digitised basis functions is an everyday task in astronomy. A general method is presented for performing such a decomposition optimally into an arbitrary set of digitised basis…
This paper was motivated by the articles "Same or different - that is the question" in CrystEngComm (July 2020) and "Change to the definition of a crystal" in the IUCr newsletter (June 2021). Experimental approaches to crystal comparisons…
A new conceptual approach for examining the origin of cosmic rays is developed by considering the characteristics of particle trajectory distributions in four-dimensional Euclidean space-time. Transformation of an isotropic distribution…
We derive the isoperimetric profile of Gaussian type for an absolutely continuous probability measure on Euclidean spaces with respect to the Lebesgue measure, whose density is a radial function.The key is a generalization of the Poincar\'e…
The analysis of Coulomb crystallization is extended from one-component to two-component plasmas. Critical parameters for the existence of Coulomb crystals are derived for both classical and quantum crystals. In the latter case, a critical…
A generalized quintessence model is presented which corresponds to a richer vacuum structure that, besides a time-dependent, slowly varying scalar field, contains a varying cosmological term. From first principles we determine a number of…
The success of present and future cosmological studies is tied to the ability to detect discrepancies in complex data sets within the framework of a cosmological model. Tensions caused by the presence of unknown systematic effects need to…
Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved…
Digital images from crystals, as projected from the third spatial dimension and recorded in atomic resolution with any kind of real-world microscope, feature necessarily broken symmetries of the translation-periodicity-restricted Euclidean…