Near-field heat transfer between graphene/hBN multilayers

We study the radiative heat transfer between multilayer structures made by a periodic repetition of a graphene sheet and a hexagonal boron nitride (hBN) slab. Surface plasmons in a monolayer graphene can couple with a hyperbolic phonon polaritons in a single hBN film to form hybrid polaritons that can assist photon tunneling. For periodic multilayer graphene/hBN structures, the stacked metallic/dielectric array can give rise to a further effective hyperbolic behavior, in addition to the intrinsic natural hyperbolic behavior of hBN. The effective hyperbolicity can enable more hyperbolic polaritons that enhance the photon tunneling and hence the near-field heat transfer. However, the hybrid polaritons on the surface, i.e. surface plasmon-phonon polaritons, dominate the near-field heat transfer between multilayer structures when the topmost layer is graphene. The effective hyperbolic regions can be well predicted by the effective medium theory (EMT), thought EMT fails to capture the hybrid surface polaritons and results in a heat transfer rate much lower compared to the exact calculation. The chemical potential of the graphene sheets can be tuned through electrical gating and results in an additional modulation of the heat transfer. We found that the near-field heat transfer between multilayer structure does not increase monotonously with the number of layer in the stack, which provides a way to control the heat transfer rate by the number of graphene layers in the multilayer structure. The results may benefit the applications of near-field energy harvesting and radiative cooling based on hybrid polaritons in two-dimensional materials.Comment: 10 pages, 11 figure

Bifurcations of families of 1D-tori in 4D symplectic maps

The regular structures of a generic 4D symplectic map with a mixed phase space are organized by one-parameter families of elliptic 1D-tori. Such families show prominent bends, gaps, and new branches. We explain these features in terms of bifurcations of the families when crossing a resonance. For these bifurcations no external parameter has to be varied. Instead, the longitudinal frequency, which varies along the family, plays the role of the bifurcation parameter. As an example we study two coupled standard maps by visualizing the elliptic and hyperbolic 1D-tori in a 3D phase-space slice, local 2D projections, and frequency space. The observed bifurcations are consistent with analytical predictions previously obtained for quasi-periodically forced oscillators. Moreover, the new families emerging from such a bifurcation form the skeleton of the corresponding resonance channel.Comment: 14 pages, 10 figures. For videos of 3D phase-space slices see http://www.comp-phys.tu-dresden.de/supp

Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a "heuristic argument" that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper "side-by-side" comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field ("time averages") are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.Comment: 52 pages, 25 figure

Pointwise Green's function bounds and stability of relaxation shocks

We establish sharp pointwise Green's function bounds and consequent linearized and nonlinear stability for smooth traveling front solutions, or relaxation shocks, of general hyperbolic relaxation systems of dissipative type, under the necessary assumptions ([G,Z.1,Z.4]) of spectral stability, i.e., stable point spectrum of the linearized operator about the wave, and hyperbolic stability of the corresponding ideal shock of the associated equilibrium system. This yields, in particular, nonlinear stability of weak relaxation shocks of the discrete kinetic Jin--Xin and Broadwell models. The techniques of this paper should have further application in the closely related case of traveling waves of systems with partial viscosity, for example in compressible gas dynamics or MHD.Comment: 120 pages. Changes since original submission. Corrected typos, esp. energy estimates of Section 7, corrected bad forward references, expanded Remark 1.17, end of introductio