Power-Law Behavior in Geometric Characteristics of Full Binary Trees

Natural river networks exhibit regular scaling laws in their topological organization. Here, we investigate whether these scaling laws are unique characteristics of river networks or can be applicable to general binary tree networks. We generate numerous binary trees, ranging from purely ordered trees to completely random trees. For each generated binary tree, we analyze whether the tree exhibits any scaling property found in river networks, i.e., the power-laws in the size distribution, the length distribution, the distance-load relationship, and the power spectrum of width function. We found that partially random trees generated on the basis of two distinct types of deterministic trees, i.e., deterministic critical and supercritical trees, show contrasting characteristics. Partially random trees generated on the basis of deterministic critical trees exhibit all power-law characteristics investigated in this study with their fitted exponents close to the values observed in natural river networks over a wide range of random-degree. On the other hand, partially random trees generated on the basis of deterministic supercritical trees rarely follow scaling laws of river networks.     

Glasses-shaped triblock copolymer prepared by combination of atom transfer radical polymerization and ring opening polymerization

A glasses-shaped triblock copolymer of poly(ε-caprolactone)-b-polystyrene-b-poly(ε-caprolactone) (PCL-b-PS-b-PCL) is prepared by combining atom transfer radical polymerization (ATRP) and ring opening polymerization (ROP). Polystyrene (PS) star polymers are prepared via ATRP using a tetra-functional initiator, followed by azidation to yield azide end-functionalized star polymers. An alkyne-functionalized coupling agent, 2,2-bis[(2-propyn-1-yloxy)methyl]-1-propanol is employed to produce hydroxy 8-shaped PS via copper(I)-catalyzed alkyne-azide cycloaddition. Herein, hydroxy 8-shaped PS with high purity is obtained through preparative size exclusion chromatography (Prep SEC) and high-performance liquid chromatography, followed by the characterizations using matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS), size exclusion chromatography (SEC), infrared, and proton nuclear magnetic resonance (¹H NMR) spectroscopy. The hydroxy groups of the 8-shaped PS are utilized as initiators for the ROP of ε-caprolactone to obtain linear chains attached to the 8-shaped architecture. After SEC fractionation, the glasses-shaped triblock copolymer is characterized using ¹H NMR and SEC. This unprecedented topology possesses two free chain-ends and two cycles; thus, both the properties of linear and cyclic polymers may be expected to be observed.     

Detection of the gravitomagnetic field using an orbiting superconducting gravity gradiometer: principle and experimental considerations

The angular momentum of the Earth produces gravitomagnetic components of the Riemann curvature tensor, which are of the order of 10⁻¹⁰ of the Newtonian terms arising from the mass of the Earth. Due to the dragging of the local inertial frame by the spinning Earth, there are also secular terms, which grow in time. These fields can be detected in principle by a set of orbiting superconducting gravity gradiometers. The Riemann tensor components for various spacecraft orientations have been computed and the principle of detecting the gravitomagnetic tidal force has been published. In this paper, we review the conclusions of the earlier analyses and discuss the feasibility of the gravity gradiometer experiment.     

Stereoscopic PIV measurements of flow around a marine propeller

A stereoscopic PIV (Particle Image Velocimetry) technique has been employed to measure the 3 dimensional flow structure of turbulent wake behind a marine propeller with 5 blades. The out-of-plane velocity component was measured using particle images captured simultaneously by two CCD cameras installed in the angular displacement configuration. 400 instantaneous velocity fields were acquired for each of four different blade phases of 0°, 18°, 36° and 54°. They were ensemble averaged to investigate the spatial evolution of propeller wake in the near wake region up to one propeller diameter (D) downstream. The phase-averaged velocity fields show clearly the viscous wake formed by the boundary layers developed along both surfaces of the blade. Tip vortices were generated periodically and the slipstream contraction occurs in the near-wake region. The out-of-plane velocity component has large values at the locations of tip and trailing vortices. With going downstream, the axial turbulence intensity and the strength of tip vortices were decreased due to the viscous dissipation, turbulence diffusion and blade-to-blade interaction. The difference in the mean velocity fields measured by SPIV and 2-D PIV methods was about 5% ≈ 10%. However, the 2-D PIV results also give sufficient information on propeller wake beyond the region of X/D=0.2.