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We show that the entropy of a finitely generated pseudogroup (resp., of a foliation of a compact Riemannian manifold) can be calculated by suitable counting separated pseudo-orbits (resp., pseudoleaves).
We present a new approach for the mechanically consistent modelling and simulation of fluid-structure interactions with contact. The fundamental idea consists of combining a relaxed contact formulation with the modelling of seepage through…
The paper aims at investigating perturbative quantum field theory (pQFT) in the approach of Epstein and Glaser (EG) and, in particular, its formulation in the language of graphs and Hopf algebras (HAs). Various HAs are encountered, each one…
We show that for a taut foliation F with one-sided branching of an atoroidal 3-manifold M, one can construct a pair of genuine laminations with solid torus complementary regions which bind every leaf of F in a geodesic lamination. These…
Bulk-edge correspondence is a cornerstone in topological physics, establishing a connection between the number of unidirectional edge modes in physical space and a Chern number, an integer that counts phase singularities of the eigenmodes…
We propose a simple model for a motor that generates mechanical motion by exploiting an entropic force arising from the topology of the underlying phase space. We show that the generation of mechanical forces in our system is surprisingly…
Flexible broad leaves are thought to reconfigure in the wind and water to reduce the drag forces that act upon them. Simple mathematical models of a flexible beam immersed in a two-dimensional flow will also exhibit this behavior. What is…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
Reconstruction of signals from compressively sensed measurements is an ill-posed problem. In this paper, we leverage the recurrent generative model, RIDE, as an image prior for compressive image reconstruction. Recurrent networks can model…
The breaking and enforcing of symmetries is a crucial ingredient in designing topologically robust materials. While magnetic fields can break time-reversal symmetry to create Chern insulators in electronic and microwave systems, at optical…
Gaseous layers (plastrons) trapped on the surfaces of immersed hydrophobic surfaces are critical for their function. Fibrillar morphologies offer a natural pathway, yet they are limited to a narrow range of liquid-surface systems and are…
An efficient algorithm for computing the branching structure of a compact Riemann surface defined via an algebraic curve is presented. Generators of the fundamental group of the base of the ramified covering punctured at the discriminant…
The approach to calculating the effective dielectric and magnetic response in bounded composite materials is developed. The method is essentially based on the renormalisation of the dielectric matrix parameters to account for the surface…
We prove a cyclic Lefschetz formula for foliations. To this end, we define a notion of equivariant cyclic cohomology and show that its expected pairing with K-theory is well defined. This enables to associate to any invariant transverse…
We show that on any Riemann surface S of genus g>1 any nonsingular even spin bundle defines e-foloation of S. When a surface is hyperelliptic then all leaves of this foliation are finite and almost all of them consists of 2g+2 points.…
We demonstrate that there exists a continuum Hamiltonian $H(\bf{r},\bf{p})$ that is formally the operator equivalent of the general tight-binding method, inheriting the associativity and Hermiticity of the latter operator. This provides a…
We examine the fracture mechanics of tearing graphene. We present a molecular dynamics simulation of the propagation of cracks in clamped, free-standing graphene as a function of the out-of-plane force. The geometry is motivated by…
This article extends a strong averaging principle for L\'evy diffusions which live on the leaves of a foliated manifold subject to small transversal L\'evy type perturbation to the case of non-compact leaves. The main result states that the…
We demonstrate the irreversibility of a wide class of world-sheet renormalization group (RG) flows to first order in $\alpha'$ in string theory. Our techniques draw on the mathematics of Ricci flows, adapted to asymptotically flat target…
We analyze the "higher rank" gauge theories, that capture some of the phenomenology of the Fracton order. It is shown that these theories lose gauge invariance when arbitrarily weak and smooth curvature is introduced. We propose a…