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

A quantitative study of the blade passing frequency noise of a centrifugal fan

Tonal noise constitutes the major part of the overall fan noise, particularly the blade passing frequency (BPF) noise, which is generally the most annoying component. This paper quantitatively studies the BPF tonal noise of a centrifugal fan, including casing aerodynamic noise, blade aerodynamic noise and casing structural noise. Firstly, fan noise generation and propagation is discussed and the measured spectra of fan noise and casing vibration are presented. Secondly, a fully 3-D transient simulation of the internal flow field of the fan is performed. Flow interactions between the impeller and the volute casing result in the periodic pressure fluctuations on solid walls of the impeller and casing. This pressure fluctuation, in the aeroacoustic study, is modeled as aeroacoustic dipole source according to the Lighthill’s acoustic analogy theory. With the inhomogeneous wave equations solved by the boundary element method, the BPF casing and blade aerodynamic noise radiation is obtained. Finally, in the casing structural noise study, the casing structural vibration under the excitation of BPF pressure fluctuation is calculated by the finite element method and sound radiation is solved by the boundary element method subsequently. Results demonstrate that the casing aerodynamic noise is the main contribution to the centrifugal fan noise with the sound power level of 103 dB followed by the blade noise (91 dB), and the casing structural noise is 79 dB

Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems

The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of conceptual importance, but also provide great opportunities towards experimental realization since space group symmetries naturally exist for any realistic material. In this paper, we systematically classify the crystalline topological superconductors (TSC) and topological insulators (TI) in 2D interacting fermionic systems by using an explicit real-space construction. In particular, we discover an intriguing fermionic crystalline topological superconductor that can only be realized in interacting fermionic systems (i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for generic 2D interacting fermionic systems.Comment: 39+37 pages, 10+13 figures, 3+1 tables, all comments and suggestions are very welcom