Global well-posedness for the Gross-Pitaevskii equation with an angular momentum rotational term in three dimensions

In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an angular momentum rotational term in which the angular velocity is equal to the isotropic trapping frequency in the space \Real^3.Comment: 11 page

Exponential Stability of the Inhomogeneous Navier-Stokes-Vlasov System in Vacuum

The main purpose of the present paper is to study the influence of the vacuum on the asymptotic behaviors of solutions to the inhomogeneous Navier-Stokes-Vlasov system in $\mathbb{R}^3\times\mathbb{R}^3$. To this end, we establish the uniform bound of the macroscopic density associated with the distribution function and prove the global existence and uniqueness of strong solutions to the Cauchy problem with vacuum for either small initial energy or large viscosity coefficient. The uniform boundedness and the presence of vacuum enable us to show that as the time evolves, the fluid velocity decays, while the distribution function concentrates towards a Dirac measure in velocity centred at $0$, with an exponential rate

Blow up solutions to a viscoelastic fluid system and a coupled Navier-Stokes/Phase-Field system in R^2

We find explicit solutions to both the Oldroyd-B model with infinite Weissenberg number and the coupled Navier-Stokes/Phase-Field system. The solutions blow up in finite time.Comment: 5 page

Formation of Nanofoam carbon and re-emergence of Superconductivity in compressed CaC6

Pressure can tune material's electronic properties and control its quantum state, making some systems present disconnected superconducting region as observed in iron chalcogenides and heavy fermion CeCu2Si2. For CaC6 superconductor (Tc of 11.5 K), applying pressure first Tc increases and then suppresses and the superconductivity of this compound is eventually disappeared at about 18 GPa. Here, we report a theoretical finding of the re-emergence of superconductivity in heavily compressed CaC6. The predicted phase III (space group Pmmn) with formation of carbon nanofoam is found to be stable at wide pressure range with a Tc up to 14.7 K at 78 GPa. Diamond-like carbon structure is adhered to the phase IV (Cmcm) for compressed CaC6 after 126 GPa, which has bad metallic behavior, indicating again departure from superconductivity. Re-emerged superconductivity in compressed CaC6 paves a new way to design new-type superconductor by inserting metal into nanoporous host lattice.Comment: 31 pages, 12 figures, and 4 table

3-Bromo-1-(3-chloro­pyridin-2-yl)-N-(4-eth­oxy­phen­yl)-1H-pyrazole-5-carbox­amide

In the title compound, C17H14BrClN4O2, the pyrazole ring is almost coplanar with the benzene ring [dihedral angle = 0.5 (2)°], whereas the pyrazole ring is close to perpendicular to the 3-chloro­pyridine ring [dihedral angle = 73.7 (2)°]. An intra­molecular C—H⋯O hydrogen bond occurs. The dominant inter­action in the crystal packing is an N—H⋯N hydrogen bond, which generates a chain along the c axis. Weak inter­molecular C—H⋯O and C—H⋯N contacts are also observe

Study on coupling effect between the time-varying gear backlash and the different time-varying mesh parameters on the gear system

The vibration excitation of the rolling mill mainly comes from the gearbox in the process of rolling strip, and the meshing excitation is the main excitation factor of the gearbox. And the gear backlash plays an important role in the meshing excitation. However, the backlash is inevitable in the process of designing the gear system. Therefore, it is important to select the appropriate gear backlash to reduce the vibration amplitude of the gearbox, to improve the rolling speed and the quality of the steel strip. So, in this paper, the effect of the different variation amplitudes for the time-varying gear backlash (TVGB) on the vibration characteristics of the gear system under various mesh parameters is studied. A new formulation for calculating nonlinear damping and time varying meshing stiffness is applied in this coupling model. The results show that increasing of the load torque, the damping ratio, the system parameter or decreasing the directional rotation radius variation or kinematic transmission error caused the effects of variation amplitudes for the (TVGB) on the dynamic characteristics of the gear system to decrease. Test data from a gearbox experimental table verifies the accuracy of the model. The model is shown to be capable of simulating the mutually coupled effect between the backlash and the different parameters on the gear system. So, the new coupled model can be used as guide to select the appropriate gear backlash values for the rolling mill under different operating conditions