A Linear-Time Algorithm for Star-Shaped Drawings of Planar Graphs with the Minimum Number of Concave Corners

A star-shaped drawing of a graph is a straight-line drawing such that each inner facial cycle is drawn as a star-shaped polygon, and the outer facial cycle is drawn as a convex polygon. In this paper, we consider the problem of finding a star-shaped drawing of a biconnected planar graph with the minimum number of concave corners. We first show new structural properties of planar graphs to derive a lower bound on the number of concave corners. Based on the lower bound, we prove that the problem can be solved in linear time by presenting a linear-time algorithm for finding a best plane embedding of a biconnected planar graph with the minimum number of concave corners. This is in spite of the fact that a biconnected planar graph may have an exponential number of different plane embeddings.     

Capability and limitation of max- and sum-type construction of Lyapunov functions for networks of iISS systems

This paper addresses the problem of verifying stability of networks whose subsystems admit dissipation inequalities of integral input-to-state stability (iISS). We focus on two ways of constructing a Lyapunov function satisfying a dissipation inequality of a given network. Their difference from one another is elucidated from the viewpoint of formulation, relation, fundamental limitation and capability. One is referred to as the max-type construction resulting in a Lipschitz continuous Lyapunov function. The other is the sum-type construction resulting in a continuously differentiable Lyapunov function. This paper presents geometrical conditions under which the Lyapunov construction is possible for a network comprising $n\ge 2$ subsystems. Although the sum-type construction for general $n>2$ has not yet been reduced to a readily computable condition, we obtain a simple condition of iISS small gain in the case of $n=2$. It is demonstrated that the max-type construction fails to offer a Lyapunov function if the network contains subsystems which are not input-to-state stable (ISS).     

Numerical study on the effect of heat loss upon the critical marangoni number in a half-zone liquid bridge

In a half-zone (HZ) liquid bridge, flow exhibits a transition from a two-dimensional steady to a three-dimensional oscillatory flow if the Marangoni number Ma exceeds a critical value Ma_c, or ΔT>ΔT_c. In case of high Prandtle number fluids, the Mac obtained in the numerical simulations deviated significantly from the ones by the experiments. One of the causes of the difference is due to the heat loss over the free surface. Most of past researches neglected effects of the heat loss through an interface of the liquid bridge. Recently several experimental and analytical works reported that the critical condition is significantly affected by the heat loss. The present study aims to include the effects of the heat loss upon the Ma_c. As the result, the calculated Ma_c agrees well with the experiment for a high Pr fluid.     

Oxygen permeation properties and surface modification of acceptor-doped CeO2/MnFe2O4 composites

The preparation and oxygen permeation properties of the (Ce_0.8Pr_0.2)O_2−δ − x vol% MnFe₂O₄ composites, where x = 0 to 35, have been investigated. The samples were prepared by the Pechini method. In the case of Ce_0.8Pr_0.2O_2−δ, an oxygen flux density of 6 μmol⋅cm⁻²⋅s⁻¹ (L = 0.0247 cm) and the maximum methane conversion of 50% were attained at 1000^∘C. Unlike composites consisting of Gd-doped CeO₂ and MnFe₂O₄, the oxygen permeability of the (Ce_0.8Pr_0.2)O_2−δ – x vol% MnFe₂O₄ composites was almost constant regardless of the volume fraction of MnFe₂O₄; however, the optimum volume fraction of MnFe₂O₄ was determined to be 5 to 25 in the context of the chemical and mechanical stabilities under methane conversion atmosphere. In addition, the surface modification of the (Ce_0.8Gd_0.2)O_2−δ – 15 vol% MnFe₂O₄ composite was performed by using the FePt nanoparticles. The catalyst loading of 2.8 mg/cm² on the both side of the 0.3 mm-thick (Ce_0.8Gd_0.2)O_2−δ – 15vol% MnFe₂O₄ composite increased the oxygen flux density from 0.30 to 0.76 μmol⋅cm⁻²⋅s⁻¹ in the case of He/air gradients; however, the effect seems to be reduced in the case of high oxygen flux density caused by a large pO₂ gradient. Moreover, the Langmuir-Blodgett film of the FePt nanoparticles were successfully prepared on the tape-cast (Ce_0.8Gd_0.2)O_2−δ – 15vol% MnFe₂O₄ composite. Hydrophobic treatments for the surface of the composite were crucial to achieve high transfer ratio for the deposition of the LB film.     

Microstructure and yield strength of UDIMET 720LI alloyed with Co-16.9 Wt Pct Ti

We proposed a new method for developing Ni-base turbine disc alloy for application at temperatures above 700 °C by mixing a Ni-base superalloy U720LI with a two-phase alloy Co-16.9 wt pct Ti in various contents. The microstructure and phase stability of the alloys were analyzed using an optical microscope, a scanning electron microscope, energy-dispersive spectroscopy, and an X-ray diffractometer. The yield strength was studied by compression tests at temperatures ranging from 25 °C to 1200 °C. The results show that all the alloys had a dendritic structure. Ni₃Ti (η) phase was formed in the interdendritic region in the alloys with the addition of Co-16.9 wt pct Ti, and its volume fraction increased with the increase in the addition of Co-16.9 wt pct Ti. The results of exposure at 750 °C show that the addition of Co-16.9 wt pct Ti to U720LI had a great effect on suppressing the formation of σ phase due to the reduced Cr content in the γ matrix. Compared to U720LI, the alloys with the addition of Co-16.9 wt pct Ti possessed higher yield strength. The solid-solution strengthening of γ and γ′ and higher volume fraction of γ′ were assumed to cause this strength increase.     

Study on Magnetic Responsibility of Rare Earth Ferrite／Polyacrylamide Magnetic Microsphere

Magneticpolymermicrospherecanbeseparatedquicklyundermagneticfieldandithasgotwideappli cationinmanyfields ,suchascellseparationetc .Themicrospheremustpossesshighmagneticresponsibili ty ,sothatmagneticseparationisquickandconve nient.Themagneticresponsibilit…     

Numerical Cracking and Debonding Analysis of RC Beams Reinforced with FRP Sheet

Bonding a fiber reinforced polymer (FRP) sheet to the tension-side surface of reinforced concrete (RC) structures is often performed to upgrade the flexural capacity and stiffness. Except for upper concrete crushing, FRP sheet reinforcing RC structure may fail in sheet rupture, sheet peeloff failure due to opening of a critical diagonal crack, or concrete cover delamination failure from the sheet end. Accompanying the occurrence of these failure modes, reinforcing effects of the FRP sheet will be lost and load-carrying capacity of the RC structures will be decreased suddenly. This study is devoted to developing a numerical analysis method by using a three-dimensional elasto-plastic finite element method to simulate the load-carrying capacity of RC beams failed in the FRP sheet peeloff mode. Here, the discrete crack approach was employed to consider geometrical discontinuities such as opening of cracks, slipping of rebar, and debonding of the FRP sheet. Comparisons between analytical and experimental results confirm that the proposed numerical analysis method is appropriate for estimating the load-carrying capacity and failure behavior of RC beams flexurally reinforced with a FRP sheet.     

Seismic proof test of a reinforced concrete containment vessel (RCCV): Part 2: Results of shaking table tests

A 1/8-scale model was constructed of a reinforced concrete containment vessel (RCCV) used in the latest advanced boiling water reactors (ABWR). Shaking table tests were conducted on it with input motions corresponding to or exceeding a design earthquake assumed for a real Nuclear Power Plant.The objectives of the tests were to verify the structural integrity and the leak-proof functional soundness of the RCCV subjected to design earthquakes, and to determine the ultimate strength and seismic margin by an excitation that led to the model's collapse. The model, the test sequence and the pressure and leak test results were addressed in Part 1. The shaking table test method, the input motions and the test results, including the transition of the model's stiffness, natural frequencies and damping factors and the effects of vertical input motions and internal pressure on the model's characteristics and behavior, the load–deformation, the ultimate strength, the failure mode of the reinforced concrete portion and the liner plate are described here. The seismic safety margin that was evaluated by the energy input during the failure test to a design basis earthquake will be described in Part 3. The analytical results of simulation using the multi-lumped mass model will be described in Part 4.     

Shaped silicon-crystal wafers obtained by plastic deformation and their application to silicon-crystal lenses.

Plastic deformation is an unlikely process by which to mould pristine silicon wafers into three-dimensional shapes owing to the inevitable detrimental impact that the resulting mechanically induced defects would have on their electrical properties. However, if one were to find a way of doing so without substantial degradation of these properties, a range of new applications might be opened up. Here we report on the successful plastic deformation of silicon crystal wafers for the preparation of wafers with various shapes. A silicon wafer was set between dies and pressed at high temperatures. One application of shaped wafers is as well-shaped concave silicon crystal lenses or mirrors. The lattice plane of such a crystal lens has a curvature exactly along the surface. A concave spheroidal X-ray lens, in the form of two-dimensional Johann and Johansson's monochromators, is proposed for an X-ray optical component system. We propose and demonstrate a new solar cell system with the concave silicon crystal mirror used as both a solar cell and a focused mirror. This system can make use of the reflected photons from solar cells.     

Three dimensional virtual crack closure-integral method (VCCM) with skewed and non-symmetric mesh arrangement at the crack front

In this paper, an extension of virtual crack closure-integral method (VCCM) for three dimensional linear fracture mechanics analysis using hexahedron finite elements is presented. In conventional three dimensional VCCM, there are some inherent requirements on the finite element model. They are (i) the faces of finite elements across the crack front have the same areas and (ii) they must be arranged symmetrically across the crack front. In present study, we developed a three dimensional VCCM without such requirements by considering work required to open one element face area whose shape is arbitrary. Though we assume the use of an ordinary 20 node serendipity element, present approach can be applied to other types of hexahedron elements.