Related papers: Discrete Directional Gabor Frames
Graph-based methods have been proposed as a unified framework for discrete calculus of local and nonlocal image processing methods in the recent years. In order to translate variational models and partial differential equations to a graph,…
We develop a general strategy in order to implement (approximate) discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is a rectangle equipped with…
A rigidity theory is developed for bar-joint frameworks in $\mathbb{R}^{d+1}$ whose vertices are constrained to lie on concentric $d$-spheres with independently variable radii. In particular, combinatorial characterisations are established…
We present the Eulerian Gaussian beam method in anisotropic media. We derive kinematic and dynamic ray tracing equations based on the level set theory and Eulerian theory using the anisotropic eikonal equation. Compared with the traditional…
This paper is devoted to show a discrete adaptive finite element approximation result for the isotropic two-dimensional Griffith energy arising in fracture mechanics. The problem is addressed in the geometric measure theoretic framework of…
We present the first steps of a procedure which discretises surface theory in classical projective differential geometry in such a manner that underlying integrable structure is preserved. We propose a canonical frame in terms of which the…
A common numerical task is to represent functions which are highly spatially anisotropic, and to solve differential equations related to these functions. One way such anisotropy arises is that information transfer along one spatial…
The aim of this note is to present a self-contained proof of the fact that a function can be approximated using a linear combination of Gaussian coherent states, with a number of terms controlled in terms of the smoothness and of the decay…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive analytical error bounds on expectation values of system…
We consider integrable systems that are connected with orthogonal separation of variables in complex Riemannian spaces of constant curvature. An isomorphism with the hyperbolic Gaudin magnet, previously pointed out by one of us, extends to…
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…
We discuss the concepts of pseudo-dual frames and approximately dual frames, and illuminate their relationship to classical frames. Approximately dual frames are easier to construct than the classical dual frames, and might be tailored to…
This paper is devoted to discrete mechanical systems subject to external forces. We introduce a discrete version of systems with Rayleigh-type forces, obtain the equations of motion and characterize the equivalence for these systems.…
It is well known that for gradient systems in Euclidean space or on a Riemannian manifold, the energy decreases monotonically along solutions. In this letter we derive and analyse functionally fitted energy-diminishing methods to preserve…
We introduce the framework of discrete holomorphic functions on t-embeddings of weighted bipartite planar graphs; t-embeddings also appeared under the name Coulomb gauges in a recent paper arXiv:1810.05616. We argue that this framework is…
In this paper we develop constructive invertibility conditions for the twisted convolution. Our approach is based on splitting the twisted convolution with rational parameters into a finite number of weighted convolutions, which can be…
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
Let $g$ be a totally positive function of finite type. Then the Gabor set $\{e^{2\pi i \beta l t} g(t-\alpha k), k,l \in Z \}$ is a frame for $L^2(R)$, if and only if $\alpha \beta <1$. This result is a first positive contribution to a…
In this article, we generalize the theory of discrete Lagrangian mechanics and variational integrators in two principal directions. First, we show that Lagrangian submanifolds of symplectic groupoids give rise to discrete dynamical systems,…