The semi-discrete AKNS system: Conservation laws, reductions and continuum limits

In this paper, the semi-discrete Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy is shown in spirit composed by the Ablowitz-Ladik flows under certain combinations. Furthermore, we derive its explicit Lax pairs and infinitely many conservation laws, which are non-trivial in light of continuum limit. Reductions of the semi-discrete AKNS hierarchy are investigated to include the semi-discrete Korteweg-de Vries (KdV), the semi-discrete modified KdV, and the semi-discrete nonlinear Schr\"odinger hierarchies as its special cases. Finally, under the uniform continuum limit we introduce in the paper, the above results of the semi-discrete AKNS hierarchy, including Lax pairs, infinitely many conservation laws and reductions, recover their counterparts of the continuous AKNS hierarchy

Polytypism and Unexpected Strong Interlayer Coupling of two-Dimensional Layered ReS2

The anisotropic two-dimensional (2D) van der Waals (vdW) layered materials, with both scientific interest and potential application, have one more dimension to tune the properties than the isotropic 2D materials. The interlayer vdW coupling determines the properties of 2D multi-layer materials by varying stacking orders. As an important representative anisotropic 2D materials, multilayer rhenium disulfide (ReS2) was expected to be random stacking and lack of interlayer coupling. Here, we demonstrate two stable stacking orders (aa and a-b) of N layer (NL, N>1) ReS2 from ultralow-frequency and high-frequency Raman spectroscopy, photoluminescence spectroscopy and first-principles density functional theory calculation. Two interlayer shear modes are observed in aa-stacked NL-ReS2 while only one interlayer shear mode appears in a-b-stacked NL-ReS2, suggesting anisotropic-like and isotropic-like stacking orders in aa- and a-b-stacked NL-ReS2, respectively. The frequency of the interlayer shear and breathing modes reveals unexpected strong interlayer coupling in aa- and a-b-NL-ReS2, the force constants of which are 55-90% to those of multilayer MoS2. The observation of strong interlayer coupling and polytypism in multi-layer ReS2 stimulate future studies on the structure, electronic and optical properties of other 2D anisotropic materials

Five-dimensional generalized f(R)f(R) gravity with curvature-matter coupling

The generalized $f(R)$ gravity with curvature-matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal spacelike Killing vector field of 5D spacetime, and it can be reduced to the 4D formulism of FRW universe. This theory is quite general and can give the corresponding results to the Einstein gravity, $f(R)$ gravity with both no-coupling and non-minimal coupling in 5D spacetime as special cases, that is, we would give the some new results besides previous ones given by Ref.\cite{60}. Furthermore, in order to get some insight into the effects of this theory on the 4D spacetime, by considering a specific type of models with $f_{1}(R)=f_{2}(R)=\alpha R^{m}$ and $B(L_{m})=L_{m}=-\rho$, we not only discuss the constraints on the model parameters $m$, $n$, but also illustrate the evolutionary trajectories of the scale factor $a(t)$, the deceleration parameter $q(t)$ and the scalar field $\epsilon(t)$, $\phi(t)$ in the reduced 4D spacetime. The research results show that this type of $f(R)$ gravity models given by us could explain the current accelerated expansion of our universe without introducing dark energy.Comment: arXiv admin note: text overlap with arXiv:0912.4581, arXiv:gr-qc/0411066 by other author

Nearby SNR: a possible common origin to multi-messenger anomalies in spectra, ratios and anisotropy of cosmic rays

The multi-messenger anomalies, including spectral hardening or excess for nuclei, leptons, ratios of $\bar p/p$ and B/C, and anisotropic reversal, were observed in past years. AMS-02 experiment also revealed different spectral break for positron and electron at 284 GeV and beyond TeV respectively. It is natural to ask whether all those anomalies originate from one unified physical scenario. In this work, the spatially-dependent propagation (SDP) with a nearby SNR source is adopted to reproduce above mentioned anomalies. There possibly exists dense molecular cloud(DMC) around SNRs and the secondary particles can be produced by pp-collision or fragmentation between the accelerated primary cosmic rays and DMC. As a result, the spectral hardening for primary, secondary particles and ratios of $B/C$ and $\bar p/p$ can be well reproduced. Due to the energy loss at source age of 330 kyrs, the characteristic spectral break-off for primary electron is at about 1 TeV hinted from the measurements. The secondary positron and electron from charged pion take up $5\%$ energy from their mother particles, so the positron spectrum has a cut-off at $\sim$250 GeV. Therefore, the different spectral break for positron and electron together with other anomalies can be fulfilled in this unified physical scenario. More interesting is that we also obtain the featured structures as spectral break-off at 5 TV for secondary particles of Li, Be, B, which can be served to verify our model. We hope that those tagged structures can be observed by the new generation of space-borne experiment HERD in future.Comment: 16 pages, 12 figure