The Casimir force between two hyperbolic metamaterials (HMMs) constructed by alternative metal-dielectric layers is investigated. Due to the existence of the hyperbolic dispersion, the electromagnetic response of HMMs becomes extremely dramatic, which is embodied by the nearly total reflection in such frequency region. As a result, the Casimir force between HMMs is much greater than that between ordinary dielectrics. In addition, it is shown that the Casimir force is proportional to the bandwidth of this hyperbolic dispersion, which is dependent on the filling factor as well as the characteristic frequencies of ingredient materials. Therefore, the relations between the force and these parameters are discussed. We show that the Casimir force can be controlled by tuning the bandwidth possessing hyperbolic dispersion of the structures. This work provides promising applications of HMMs on microelectromechanical systems and nanoelectromechanical systems.

We propose a scheme which can generate a highly directional single photon with almost 100% efficiency. Therefore we can get a useful single photon when it is required. An initial excited atom is placed inside a special Fabry-Pérot cavity whose walls consist of left-handed and zero-index metamaterials. The left-handed slabs work as a closed shell to avoid dissipation of the emitted photon, while the outer zero-index metamaterial slabs act as a special shutter which is transparent only for normal incidence, so that the photon emitted by the atom can only escape out of the cavity unidirectionally. Furthermore, we design the cavity with currently available metamaterials made of two-dimensional dielectric photonic crystals, and simulate the radiative field of an electric dipole to confirm our prediction. Differently from the previous proposal of single-photon sources which demanded complicated structure design and subtle mode analysis, our scheme is simple and robust for atomic position. This work has promising applications for quantum communication and optical quantum computing.

Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and thus ensure that their predictions are consistent and stable with the physical laws. PINNs open up a new approach to address inverse problems in fluid mechanics. Based on the single-relaxation-time lattice Boltzmann method (SRT-LBM) with the Bhatnagar–Gross–Krook (BGK) collision operator, the PINN-SRT-LBM model is proposed in this paper for solving the inverse problem in fluid mechanics. The PINN-SRT-LBM model consists of three components. The first component involves a deep neural network that predicts equilibrium control equations in different discrete velocity directions within the SRT-LBM. The second component employs another deep neural network to predict non-equilibrium control equations, enabling the inference of the fluid’s non-equilibrium characteristics. The third component, a physics-informed function, translates the outputs of the first two networks into physical information. By minimizing the residuals of the physical partial differential equations (PDEs), the physics-informed function infers relevant macroscopic quantities of the flow. The model evolves two sub-models that are applicable to different dimensions, named the PINN-SRT-LBM-I and PINN-SRT-LBM-II models according to the construction of the physics-informed function. The innovation of this work is the introduction of SRT-LBM and discrete velocity models as physical drivers into a neural network through the interpretation function. Therefore, the PINN-SRT-LBM allows a given neural network to handle inverse problems of various dimensions and focus on problem-specific solving. Our experimental results confirm the accurate prediction by this model of flow information at different Reynolds numbers within the computational domain. Relying on the PINN-SRT-LBM models, inverse problems in fluid mechanics can be solved efficiently.

The Casimir force between electric and magnetic hyperbolic metamaterial slabs is investigated. Due to hyperbolic dispersion, the electromagnetic features of these metamaterials along the optical axis are different from those perpendicular to the optical axis; consequently, these features contribute differently to the Casimir effect. The repulsive Casimir force is formed between electric and magnetic hyperbolic metamaterial slabs; moreover, hyperbolic dispersion can enhance the repulsive effect. However, by utilizing the extremely anisotropic behavior of hyperbolic metamaterials and changing the separation distance between the two slabs, the restoring Casimir force emerges. Additionally, by considering the dispersion of both the permittivity and the permeability of hyperbolic metamaterials, the Casimir force reaches several equilibrium points at different separation distances. Furthermore, the Casimir force at room temperature is discussed. Although the temperature can weaken the effect of the restoring Casimir force, stable equilibria may remain upon choosing suitable filling factors. This work shows that hyperbolic metamaterials have potential applications in micro- and nanoelectromechanical systems, especially for maintaining stability and overcoming adhesion problems.

Understanding internal vortex breakdowns (VBs) and their trajectories in sealed cylinders are important for the scientific and industrial applications with which they are linked. However, the fluids in sealed cylinders are often sheared, which makes it difficult to clearly and multidirectionally observe their internal flow patterns simultaneously with existing experimental tools; this results in some important features not being captured. In this work, we performed thousands of numerical simulations in a sealed cylinder utilizing the finite element approach. Abundant internal VB patterns were obtained for different aspect ratios as the Reynolds number (Re) increased. To further quantitatively study the morphological evolution of VBs, we focused on the axial lengths and trajectories of VBs with multiple aspect ratios. Surprisingly, the numbers of VBs in the rotating fluid were not fixed for the same aspect ratio, which also affected the complexity of the VB evolution. In particular, the stair-step changes of the locations of the VB and local extrema of the axial velocity, pressure, and vorticity of the key flows at the axis were revealed in detail. We used the theory of swirl decay to explain the VB formation and stair-step change from an energy perspective and clarified why the pressure minimum was under the center of the VB. The discovery of the stair-step change of the VB provided evidence of the existence of a new class of fluid behavior that may provide insight into vortex control.

Quantum interference between Zeeman levels of atom placed in the structure containing left-handed materials (LHMs) and zero-index metamaterials (ZIMs) is investigated. Because of the existence of the LHM and ZIM, dipole radiation becomes highly anisotropic which is embodied by the high contrast between decay rates of the dipole component parallel to the surface and that normal to the surface. Furthermore, both decay rates are suppressed compared with those in free vacuum. Therefore, we propose the quantum interference between Zeeman levels accompanied by long lifetime. Two structures are designed to achieve such purpose. For the idealized LHM and ZIM without dissipation, a double-layer structure comprised of them is the right candidate. However, when we consider the dissipation of materials, a Fabry-P\'erot cavity made of matched ZIM slabs and LHM slabs is required. Results show that we get a high degree of quantum interference and low decay rates simultaneously.