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Porous media, while ubiquitous across many engineering disciplines, is inherently difficult to characterize due to their innate stochasticity and heterogeneity. The key for predicting porous material behavior comes down to the structuring…
The second order optical response of centrosymmetric materials manifests itself mostly at their surface, being strongly suppressed in their bulk. However, the overall surface response is also suppressed in nanoparticles with a…
Recent advances in scanning transmission electron and scanning tunneling microscopies allow researchers to measure materials structural and electronic properties, such as atomic displacements and charge density modulations, at an Angstrom…
Recently, Minkowski Tensors (MT) have gained popularity for morphological analysis tasks. As opposed to the scalar Minkowski functionals (MF; in 2D given by area, perimeter and Euler characteristic), MT can characterize symmetry and…
The Materials Project crystal structure database has been searched for materials possessing layered motifs in their crystal structures using a topology-scaling algorithm. The algorithm identifies and measures the sizes of bonded atomic…
We present measurements of the Minkowski functionals extracted from the SDSS-III BOSS catalogs. After defining the Minkowski functionals, we describe how an unbiased reconstruction of these statistics can be obtained from a field with…
Observations reveal that on large scales the universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions -- voids. This thesis reports the construction of a sophisticated computational…
Understanding structure-function relationships is essential to advance the manufacturing of next-gen materials with desired properties and functionalities. Precise and rapid measurement of features like wrinkle size, droplet diameter, and…
We measure the geometry, topology and morphology of the superclusters in mock SDSS catalogues prepared by Cole et al.(1998). The mock catalogues refer to $\tau$CDM and $\L$CDM {\em flat} cosmological models and are populated by galaxies so…
The presence of massive neutrinos affects structure formation, leaving imprints on large-scale structure observables such as the weak lensing field. The common lensing analyses with two-point statistics are insensitive to the large amount…
To study the global morphology of the galaxy distribution in our local neighbourhood we calculate the Minkowski functionals for a sequence of volume limited samples within a sphere of 8 Mpc centred on our galaxy. The well known strong…
Minkowski functionals constitute a family of order parameters which discriminate spatial patterns according to size, shape and connectivity. Here we point out, that these scalar descriptors can be complemented by vector-valued curvature…
The results of fabrication and characterization of atomic structure of nanocrystalline thin layers of Y2O3 in cubic and monoclinic phases is reported. Experimental data demonstrate crystalline ordering in nanocrystalline films with average…
Minkowski functionals provide a novel tool to characterize the large-scale galaxy distribution in the Universe. Here we give a brief tutorial on the basic features of these morphological measures and indicate their practical application for…
The study of the angular power spectrum of Cosmic Microwave Background (CMB) anisotropies, both in intensity and in polarisation, has led to the tightest constraints on cosmological parameters. However, this statistical quantity is not…
We study the morphology of convergence maps by perturbatively reconstructing their Minkowski Functionals (MFs). We present a systematics study using a set of three generalised skew-spectra as a function of source redshift and smoothing…
In order to quantify higher-order correlations of the galaxy cluster distribution we use a complete family of additive measures which give scale-dependent morphological information. Minkowski functionals can be expressed analytically in…
We investigate the cosmological information in higher-order statistics of the cosmic microwave background (CMB) lensing convergence field for a near-term experiment with noise properties similar to the Simons Observatory (SO). Using a fully…
Two-dimensional (2D) crystals are attracting growing interest in various research fields such as engineering, physics, chemistry, pharmacy and biology owing to their low dimensionality and dramatic change of properties compared to the bulk…
Minkowski functionals (MFs) are a set of statistics that characterise the geometry and topology of the cosmic density field and contain complementary information to the standard two-point analyses. We present MEDUSA, an implementation of an…