Related papers: Discrete Tomography of Planar Model Sets
The model is a particular case of causal set. This is a discrete model of spacetime in a microscopic level. In paper the most general properties of the model are investigated without any reference to a dynamics. The dynamics of the model is…
Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack…
We present a generalization of the coupled dipole method to the scattering of light by arbitrary periodic structures. This new formulation of the coupled dipole method relies on the same direct-space discretization scheme that is widely…
In this paper we use families of finite subgroups to study Grothendieck rings associated to certain discrete groups, such as the arithmetic ones.
We introduce a discretization scheme for continuous localized frames using quasi-Monte Carlo integration and discrepancy theory. By generalizing classical concepts, we define a discrepancy measure on the entire phase space $\mathbb{R}^2$…
Discrete-value time series are sequences of measurements where each measurement is a discrete (categorical or integer) value. These time series are widely used in various fields, and their classification and clustering are essential for…
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular,…
A sparse modeling approach is proposed for analyzing scanning tunneling microscopy topography data, which contains numerous peaks corresponding to surface atoms. The method, based on the relevance vector machine with $\mathrm{L}_1$…
Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing…
In the segmentation of fine-scale structures from natural and biomedical images, per-pixel accuracy is not the only metric of concern. Topological correctness, such as vessel connectivity and membrane closure, is crucial for downstream…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction…
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
A class of quasilinear singularly perturbed boundary value problems with a turning point of attractive type is considered. The problems are solved numerically by a finite-difference scheme on a special discretization mesh which is dense…
The topic of these notes could be easily expanded into a full one-semester course. Nevertheless, we shall try to give some flavour along with theoretical bases of spectral and pseudo-spectral methods. The main focus is made on Fourier-type…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…
Diffraction tomography is an inverse scattering technique used to reconstruct the spatial distribution of the material properties of a weakly scattering object. The object is exposed to radiation, typically light or ultrasound, and the…
Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent…
The purpose of this work is the development and determination of higher-order continuum-like kinematic measures which characterize discrete kinematic data obtained from experimental measurement (e.g., digital image correlation) or kinematic…