Apparent horizon and gravitational thermodynamics of Universe in the Eddington-Born-Infeld theory

The thermodynamics of Universe in the Eddington-Born-Infeld (EBI) theory was restudied by utilizing the holographic-style gravitational equations that dominate the dynamics of the cosmical apparent horizon $\Upsilon_{A}$ and the evolution of Universe. We started in rewriting the EBI action of the Palatini approach into the Bigravity-type action with an extra metric $q_{\mu\nu}$. With the help of the holographic-style dynamical equations, we discussed the property of the cosmical apparent horizon $\Upsilon_{A}$ including timelike, spacelike and null characters, which depends on the value of the parameter of state $w_{m}$ in EBI Universe. The unified first law for the gravitational thermodynamics and the total energy differential for the open system enveloped by $\Upsilon_{A}$ in EBI Universe were obtained. Finally, applying the positive-heat-out sign convention, we derived the generalized second law of gravitational thermodynamics in EBI universe.Comment: 23 pages, 0 figure

Dirac series of E7(−5)E_{7(-5)}

Using the sharpened Helgason-Johnson bound, this paper classifies all the irreducible unitary representations with non-zero Dirac cohomology of $E_{7(-5)}$. As an application, we find that the cancellation between the even part and the odd part of the Dirac cohomology continues to happen for certain unitary representations of $E_{7(-5)}$. Assuming the infinitesimal character being integral, we further improve the Helgason-Johnson bound for $E_{7(-5)}$. This should help people to understand (part of) the unitary dual of this group.Comment: 25 pages. arXiv admin note: text overlap with arXiv:2204.0790

Atomically Sharp, Closed Bilayer Phosphorene Edges by Self-Passivation

Two-dimensional (2D) crystals' edge structures not only influence their overall properties but also dictate their formation due to edge-mediated synthesis and etching processes. Edges must be carefully examined because they often display complex, unexpected features at the atomic scale, such as reconstruction, functionalization, and uncontrolled contamination. Here, we examine atomic-scale edge structures and uncover reconstruction behavior in bilayer phosphorene. We use in situ transmission electron microscopy (TEM) of phosphorene/graphene specimens at elevated temperatures to minimize surface contamination and reduce e-beam damage, allowing us to observe intrinsic edge configurations. Bilayer zigzag (ZZ) edge was found the most stable edge configuration under e-beam irradiation. Through first-principles calculations and TEM image analysis under various tilting and defocus conditions, we find that bilayer ZZ edges undergo edge reconstruction and so acquire closed, self-passivated edge configurations. The extremely low formation energy of the closed bilayer ZZ edge and its high stability against e-beam irradiation are confirmed by first-principles calculations. Moreover, we fabricate bilayer phosphorene nanoribbons with atomically-sharp closed ZZ edges. The identified bilayer ZZ edges will aid in the fundamental understanding of the synthesis, degradation, reconstruction, and applications of phosphorene and related structures.Comment: 22 pages, 5 figure

Electromagnetic modeling of anisotropic medium and applications

4 pagesA stable method of calculation of the electromagnetic response of planar anisotropic laminates to an active source with limited distribution along the strata direction is developed. The laminates can be sandwiched between isotropic, anisotropic, or perfectly conducting covers/substrates. The source is either inside the laminates or in the cover or substrate. Based on the propagator matrix method, the proposed method relies on downward- and upward-going recurrence relations which transfer the tangential electric and magnetic fields from one interface to the next in accord with the boundary conditions, even when an distributed active source is embedded between the two interfaces. The electromagnetic response of general anisotropic laminates to active sources within or above them can thus be efficiently and accurately computed without further consideration of the conventional numerical instability issue. Some focus is put also on the highly practical case of electrically uniaxial materials with anisotropy axes parallel with the strata (fiber-reinforced composite panels). The method works for conductive and dielectric materials, and from eddy-currents to microwaves, without specific tuning, as it will be illustrated in the presentation by a number of examples in comparison to the literature. Once the incident field in a non-damaged structure has been obtained, then the case of a damaged layered structure is handled via a method of moments based on rectilinear discretization and windowing. The numerical approach is validated with comparisons to known results (isotropic case) and FEM computations (isotropic and anisotropic cases), illustrating efficiency and accuracy