Related papers: Vicinal Surfaces, Fractional Statistics and Univer…
We investigate homological stability for the space of sections of Fano fibrations over curves in the context of weak approximation, and establish it for projective bundles, as well as for conic and quadric surface bundles over curves.
We classify fibrations by integral plane projective rational quartic curves whose generic fibre is regular but admits a non-smooth point that is a canonical divisor. These fibrations can only exist in characteristic two. The geometric…
One standard approach to describe the collective behaviour of self-propelled particles is the Vicsek model: point-like self-propelled particles tend to align their migration directions to the ones of their nearer neighbours at each…
The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one-phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions $n\geq3$ is completely open. In…
In this article, we study and analyze the \phi-sectional curvature induced by a statistical structure on an almost contact metric manifold. We demonstrate that this sectional curvature is always non-positive. Additionally, we present…
Fuzzy geometry considered as the possible mathematical framework for reformulation of quantum-mechanical formalism in geometric terms. In this approach the states of massive particle m correspond to elements of fuzzy manifold called fuzzy…
The off-diagonal profile phi(v) associated with a local operator (order parameter or energy density) close to the boundary of a semi-infinite strip with width L is obtained at criticality using conformal methods. It involves the surface…
Step patterns on vicinal $(2\times1)$ reconstructed surfaces of noble metals Au(110) and Pt(110), miscut towards the (100) orientation, are investigated. The free energy of the reconstructed surface with a network of crossing opposite steps…
The phase diagram of two interacting planar arrays of directed lines in random media is obtained by a renormalization group analysis. The results are discussed in the contexts of the roughening of reconstructed crystal surfaces, and the…
The main goal of this article is to understand the trace properties of nonlocal minimal graphs in~$\R^3$, i.e. nonlocal minimal surfaces with a graphical structure. We establish that at any boundary points at which the trace from inside…
The well-known phase structure of the two-dimensional sine-Gordon model is reconstructed by means of its renormalization group flow, the study of the sensitivity of the dynamics on microscopic parameters. Such an analysis resolves the…
Bosonization describes Fermi surface dynamics in terms of a collective field that lives on a part of phase space. While sensible semiclassically, the challenge of treating such a field quantum mechanically has prevented bosonization from…
Interface states in a silicon/barrier junction break the silicon valley degeneracy near the interface, a desirable feature for some Si quantum electronics applications. Within a minimal multivalley tight-binding model in one dimension, we…
A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…
The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the noise is irrelevant in such cases. Kinetic roughening is…
The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…
A polygonal surface in the pseudo-hyperbolic space H^(2,n) is a complete maximal surface bounded by a lightlike polygon in the Einstein universe Ein^(1,n) with finitely many vertices. In this article, we give several characterizations of…
In this paper we develop a common theoretical framework for the dynamics of thin featureless interfaces. We explicitly demonstrate that the same phase field and velocity dependent one-scale models characterizing the dynamics of relativistic…
We propose a generalization of Claudel, Virbhadra, and Ellis photon surfaces to the case of massive charged particles, considering a timelike hypersurface such that any worldline of a particle with mass $m$, electric charge $q$ and fixed…
The occurrence of strong coupling or nonlinear scaling behavior for kinetically rough interfaces whose dynamics are conserved, but not necessarily variational, remains to be fully understood. Here we formulate and study a family of…