Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

Effect of Streamline Curvature on Three-Dimensionality of Transitional Near-Wall Flow in a Linear Hydrofoil Cascade: A DNS Investigation

Flow, Turbulence and Combustion - The laminar flow on a curved surface transits to turbulent induced by streamline curvature which generates pressure gradient field and separated shear layer flow....     

Synthesis,structures, and electrochemistry of diiron toluene-3,4-dithiolate complexes containing phosphine ligands

Transition Metal Chemistry - In this paper, four diiron toluene-3,4-dithiolate complexes with phosphine ligands were synthesized and characterized. Treatment of complex...     

Collisional dynamics of symmetric two-dimensional quantum droplets

The collisional dynamics of two symmetric droplets with equal intraspecies scattering lengths and particle number density for each component is studied by solving the corresponding extended Gross−Pitaevskii equation in two dimensions by including a logarithmic correction term in the usual contact interaction. We find the merging droplet after collision experiences a quadrupole oscillation in its shape and the oscillation period is found to be independent of the incidental momentum for small droplets. With increasing collision momentum the colliding droplets may separate into two, or even more, and finally into small pieces of droplets. For these dynamical phases we manage to present boundaries determined by the remnant particle number in the central area and the damped oscillation of the quadrupole mode. A stability peak for the existence of droplets emerges at the critical particle numberN_c ≃ 48 for the quasi-Gaussian and flat-top shapes of the droplets.     

Robust construction of minimal surface from general initial mesh

We analyze three commonly used energy functions in solving Plateau-Mesh Problem, that is, Dirichlet, area, and the discrete mean curvature(DMC)They all possess unique advantages compared to others, but their drawbacks restrict their usages individuallyOur algorithm combines the three steps together to make full use of their featuresAt first the Dirichlet energy is optimized for faster approximation with better topologyThen the area energy is used to come close to the constrained domainFinally the DMC energy is engaged to achieve a better converging stepResults show that our method can work under a rather noisy initial mesh, which is even topologically different from the final result.     

Preparation of two-dimensional molybdenum disulfide for NO2 detection at room temperature

In this work, the two-dimensional MoS₂ film was prepared by sulfuring the molybdenum atomic layer on SiO₂/Si substrate. The reaction temperature, heating rate, holding time and carrier gas flow rate were investigated comprehensively. The quality of MoS₂ film was characterized by optical microscopy, atomic force microscopy, Raman and photoluminescence spectroscopy. The characterization results showed that the optimum synthesis parameters were heating rate of 25 °C/min, reaction temperature of 750 °C, holding time of 30 min and carrier gas velocity of 100 sccm. The MoS₂ gas sensor was fabricated and its gas sensing performance was tested. The test results indicated that the sensor had a good response to both reducing gas (NH₃) and oxidizing gas (NO₂) at room temperature. The sensitivity to 100 ppm of NO₂ was 31.3%, and the response/recovery times were 4 s and 5 s, respectively. In addition, the limit of detection could be as low as 1 ppm. This work helps us to develop low power and integrable room temperature NO₂ sensors.     

Heteroleptic [Cu(NN)P2]+-type cuprous complexes and their structural modulation on phosphorescent color: Synthesis,structural characterization,properties, and theoretical calculations

Four new heteroleptic [Cu(NN)P₂]⁺-type cuprous complexes— 1 -TPP, 2 -POP, 3 -Xantphos, and 4 -DPPF—were designed and synthesized using a diimine ligand 2-(2′-pyridyl)benzoxazole (2-PBO) and different phosphine ligands (TPP, triphenylphosphine; POP, bis[2-(diphenylphosphino)phenyl]ether; Xantphos, 4,5-bis(diphenylphosphino)-9,9-dimethylxanthene; DPPF, 1,1′-bis(diphenylphosphino)-ferrocene). All complexes were characterized using single-crystal X-ray diffraction, spectroscopic analysis (infrared, UV–Vis.), elemental analysis, and photoluminescence (PL). Single-crystal X-ray diffraction revealed complexes 1 – 4 as isolated cation complex structures with a tetrahedral CuN₂P₂ coordination geometry and diverse P–Cu–P angles. Their UV–Vis. absorption spectra exhibited a blue-shift sequence in wavelength with an enlarged P–Cu–P angle from 4 to 2 then to 3 and then to 1 . The PL emission peaks of 1 – 3 also exhibited a similar blue-shift sequence ( 2 → 3 → 1 ). Their PL lifetime in microseconds (~7.5, 5.1, and 4.7 μs for 1 , 2 , and 3 , respectively) indicated that their PL behavior represents phosphorescence. Time-dependent density functional theory (TD-DFT) calculation and wavefunction analysis revealed that S₁ and T₁ states of 1 – 3 should be assigned as metal–ligand and ligand–ligand charge-transfer (ML + L'L)CT states. Their UV–Vis. absorption and phosphorescence should be attributed to the charge transfer from the P–Cu–P segment to the 2-PBO ligand. Therefore, as the P–Cu–P angle increased (lower HOMO), the energy of S₁ and T₁ states also increased, following the change of PL color.