Related papers: Computational explorations of a deformed fuzzy sph…

A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator. Examples include fuzzy…

We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a surface in $\mathbb{R}^3$. We find that several surfaces,…

The properties of the phi^4 scalar field theory on a fuzzy sphere are studied numerically. The fuzzy sphere is a discretization of the sphere through matrices in which the symmetries of the space are preserved. This model presents three…

This thesis is devoted to the study of Quantum Field Theories (QFT) on fuzzy spaces. Fuzzy spaces are approximations to the algebra of functions of a continuous space by a finite matrix algebra. In the limit of infinitely large matrices the…

Spectral triples on the q-deformed spheres of dimension two and three are reviewed.

The techniques developed for matrix models and fuzzy geometry are powerful tools for representing strings and membranes in quantum physics. We study the representation of fuzzy surfaces using these techniques. This involves constructing…

The phi^4 real scalar field theory on a fuzzy sphere is studied numerically. We refine the phase diagram for this model where three distinct phases are known to exist: a uniformly ordered phase, a disordered phase, and a non-uniform ordered…

This is an experimental case study in real algebraic geometry, aimed at computing the image of a semialgebraic subset of 3-space under a polynomial map into the plane. For general instances, the boundary of the image is given by two highly…

We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized…

The problem of constructing flexible stochastic models to describe the variability in shape of solid particles is challenging. Natural objects often exhibit mono- or multi-fractal features, i.e. irregular shapes and self-similar patterns.…

We analyze the expansion of the fuzzy sphere non-commutative product in powers of the non-commutativity parameter. To analyze this expansion we develop a graphical technique that uses spin networks. This technique is potentially interesting…

We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix model deformed by terms involving fixed…

Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis,…

A fuzzy circle and a fuzzy 3-sphere are constructed as subspaces of fuzzy complex projective spaces, of complex dimension one and three, by modifying the Laplacians on the latter so as to give unwanted states large eigenvalues. This leaves…

We study the q-deformed fuzzy sphere, which is related to D-branes on SU(2) WZW models, for both real q and q a root of unity. We construct for both cases a differential calculus which is compatible with the star structure, study the…

Three particles floating on a fluid surface define a triangle. The aim of this paper is to characterise the shape of the triangle, defined by two of its angles, as the three vertices are subject to a complex or turbulent motion. We consider…

Using the Surface Evolver software, we perform numerical simulations of point-like deformations in a two-dimensional foam. We study perturbations which are infinitesimal or finite, isotropic or anisotropic, and we either conserve or do not…

We consider the quantum computational process as viewed by an insider observer: this is equivalent to an isomorphism between the quantum computer and a quantum space, namely the fuzzy sphere. The result is the formulation of a reversible…

We study mathematical and computational models for computing the deformation of fiber-reinforced cross-plied laminates due to external forces. This requires an understanding of both micro-structural effects and different sources of…

Fuzzy spaces like the fuzzy sphere or the fuzzy torus have received remarkable attention, since they appeared as objects in string theory. Although there are many higher dimensional examples, the most known and most studied fuzzy spaces are…