Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports.Comment: 4 figure

Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map

In contrary to other 1D momentum-conserving lattices such as the Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) lattice, the 1D coupled rotator lattice is a notable exception which conserves total momentum while exhibits normal heat conduction behavior. The temperature behavior of the thermal conductivities of 1D coupled rotator lattice had been studied in previous works trying to reveal the underlying physical mechanism for normal heat conduction. However, two different temperature behaviors of thermal conductivities have been claimed for the same coupled rotator lattice. These different temperature behaviors also intrigue the debate whether there is a phase transition of thermal conductivities as the function of temperature. In this work, we will revisit the temperature dependent thermal conductivities for the 1D coupled rotator lattice. We find that the temperature dependence follows a power law behavior which is different with the previously found temperature behaviors. Our results also support the claim that there is no phase transition for 1D coupled rotator lattice. We also give some discussion about the similarity of diffusion behaviors between the 1D coupled rotator lattice and the single kicked rotator also called the Chirikov standard map.Comment: 6 pages, 5 figure

Thermal conductance of the coupled-rotator chain: Influence of temperature and size

Thermal conductance of a homogeneous 1D nonlinear lattice system with neareast neighbor interactions has recently been computationally studied in detail by Li et al [Eur. Phys. J. B {\bf 88}, 182 (2015)], where its power-law dependence on temperature $T$ for high temperatures is shown. Here, we address its entire temperature dependence, in addition to its dependence on the size $N$ of the system. We obtain a neat data collapse for arbitrary temperatures and system sizes, and numerically show that the thermal conductance curve is quite satisfactorily described by a fat-tailed $q$-Gaussian dependence on $TN^{1/3}$ with $q \simeq 1.55$. Consequently, its $T \to\infty$ asymptotic behavior is given by $T^{-\alpha}$ with $\alpha=2/(q-1) \simeq 3.64$.Comment: 5 pages including 2 figure

Thermal rectification and negative differential thermal resistance in lattices with mass gradient

We study thermal properties of one dimensional(1D) harmonic and anharmonic lattices with mass gradient. It is found that the temperature gradient can be built up in the 1D harmonic lattice with mass gradient due to the existence of gradons. The heat flow is asymmetric in the anharmonic lattices with mass gradient. Moreover, in a certain temperature region the {\it negative differential thermal resistance} is observed. Possible applications in constructing thermal rectifier and thermal transistor by using the graded material are discussed.Comment: 4 pages 5 eps figs. Accepted for pub. in Phys. Rev. B Rap. Com