We review the near-field radiative heat flux between hyperbolic materials focusing on multilayer hyperbolic meta-materials. We discuss the formation of the hyperbolic bands, the impact of ordering of the multilayer slabs, as well as the impact of the first single layer on the heat transfer. Furthermore, we compare the contribution of surface modes to that of hyperbolic modes. Finally, we also c...

Suppose M is a compact surface and Λ ⊂ M is a nontrivial mixing hyperbolic attractor for some f ∈ Diff(M). We show that if Λ is a hyperbolic set for some g ∈ Diff(M), then Λ is a nontrivial mixing hyperbolic attractor or repeller for g.

It is a well-known fact that every Riemann surface with negative Euler characteristic admits a hyperbolic metric. But this metric is by no means unique – indeed, there are uncountably many such metrics. In this paper, we study the space of all such hyperbolic structures on a Riemann surface, called the Teichmüller space of the surface. We will show that it is a complete metric space, and that i...

The present paper studies the possibility of propagation of torsional surface waves in an inhomogeneous anisotropic layer lying between two heterogeneous half-spaces (upper and lower half-space). Both the half-spaces are assumed to be under compressive initial stress. The study reveals that under the assumed conditions, a torsional surface wave propagates in the medium. The dispersion relation ...

In autumn 1993, in front of the MSRI in Berkeley, a marble sculpture by Helaman Ferguson called The Eightfold Way was revealed. This sculpture shows a compact Riemann surface of genus 3 with tetrahedral symmetry and with a tessellation by 24 distorted heptagons. The base of the sculpture is a disc which is tessellated by hyperbolic 120◦-heptagons thus suggesting that one should imagine that the...

This work uses the dual-phase-lag (DPL) model of heat conduction to demonstrate the effect of temperature gradient relaxation time on the result of non-Fourier hyperbolic conduction in a finite slab subjected to a periodic thermal disturbance. DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. For the ...

Constructing smooth freeform surfaces of arbitrary topology with higher order continuity is one of the most fundamental problems in shape and solid modeling. Most real-world surfaces are with negative Euler characteristic number χ = 2 − 2g − b < 0, where g is genus, b is the number of boundaries. This paper articulates a novel method to construct C∞ smooth surfaces with negative Euler numbers b...

Constructing smooth freeform surfaces of arbitrary topology with higher order continuity is one of the most fundamental problems in shape and solid modeling. Most real-world surfaces are with negative Euler characteristic χ < 0. This paper articulates a novel method to construct C∞ smooth surfaces with negative Euler numbers based on hyperbolic geometry and discrete curvature flow. According to...

We consider “hyperideal” circle patterns, i.e. patterns of disks which do not cover the whole surface, which are associated to hyperideal hyperbolic polyhedra. The main result is that, on a Euclidean or hyperbolic surface with conical singularities, those hyperideal circle patterns are uniquely determined by the intersection angles of the circles and the singular curvatures. This is related to ...