Stable marker-particle method for the Voronoi diagram in a flow field

The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points.     

Finite Modules of Finite Injective Dimension Over a Noetherian Algebra

Let R be a commutative Noetherian ring. Let P(R) (respectively,I(R)) be the category of all finite R-modules of finite projective(respectively, injective) dimension. Sharp [9] constructed acategory equivalence between I(R) and P(R) for certain Cohen–Macaulaylocal rings R. Thus many properties about finite modules offinite projective dimension can be connected with those of finiteinjective dimension through this equivalence.     

On the identification of degenerate indices in the nonlinear complementarity problem with the proximal point algorithm

In this paper we focus on the problem of identifying the index sets P(x):=i|x_i>0, N(x):={i|F_i(x)>0 and C(x):=i|x_i=F_i(x)=0} for a solution x of the monotone nonlinear complementarity problem NCP(F). The correct identification of these sets is important from both theoretical and practical points of view. Such an identification enables us to remove complementarity conditions from the NCP and locally reduce the NCP to a system which can be dealt with more easily. We present a new technique that utilizes a sequence generated by the proximal point algorithm (PPA). Using the superlinear convergence property of PPA, we show that the proposed technique can identify the correct index sets without assuming the nondegeneracy and the local uniqueness of the solution.This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan.Mathematics Subject Classification (2000): 90C33, 65K10     

A large deviation principle for (r,p)-capacities on the Wiener space

Summary We formulate and prove a large deviation principle for the (r, p)-capacity on an abstract Wiener space. As an application, we obtain a sharpening of Strassen's law of the iterated logarithm in terms of the capacity.     

Branching Random Walks in Space–Time Random Environment: Survival Probability,Global and Local Growth Rates

We study the survival probability and the growth rate for branching random walks in random environment (BRWRE). The particles perform simple symmetric random walks on the d-dimensional integer lattice, while at each time unit, they split into independent copies according to time–space i.i.d. offspring distributions. The BRWRE is naturally associated with the directed polymers in random environment (DPRE), for which the quantity called the free energy is well studied. We discuss the survival probability (both global and local) for BRWRE and give a criterion for its positivity in terms of the free energy of the associated DPRE. We also show that the global growth rate for the number of particles in BRWRE is given by the free energy of the associated DPRE, though the local growth rate is given by the directional free energy.     

Acoustic energy harvesting using an electromechanical Helmholtz resonator

This paper presents the development of an acoustic energy harvester using an electromechanical Helmholtz resonator (EMHR). The EMHR consists of an orifice, cavity, and a piezoelectric diaphragm. Acoustic energy is converted to mechanical energy when sound incident on the orifice generates an oscillatory pressure in the cavity, which in turns causes the vibration of the diaphragm. The conversion of acoustic energy to electrical energy is achieved via piezoelectric transduction in the diaphragm of the EMHR. Moreover, the diaphragm is coupled with energy reclamation circuitry to increase the efficiency of the energy conversion. Lumped element modeling of the EMHR is used to provide physical insight into the coupled energy domain dynamics governing the energy reclamation process. The feasibility of acoustic energy reclamation using an EMHR is demonstrated in a plane wave tube for two power converter topologies. The first is comprised of only a rectifier, and the second uses a rectifier connected to a flyback converter to improve load matching. Experimental results indicate that approximately 30 mW of output power is harvested for an incident sound pressure level of 160 dB with a flyback converter. Such power level is sufficient to power a variety of low power electronic devices.     

Second Harmonic Generation in Bis Typed Organic Compounds

In systematic research on a series of new nonlinear organic materials, we found that Bis (4-nitrophenoxy) methane (BNPM) showed a large intensity of second harmonic light, which was 4.4 times as large as that of urea crystal by powder technique and easily crystallized from a solution. The crystal structure of BNPM, obtained by the X-ray diffraction method, was orthorhombic, space group P2₁2₁2 (point group 222), with unit-sell dimension a = 10.205 Å; b = 12.854 Å; c = 4.8822 Å. In addition, we found that the absorption edge of BNPM was 430 nm with a 0.9-mm-thick crystal, and we observed the second harmonic light with BNPM single crystal at the wavelength of 1064 nm and in the range from 906 nm to 990 nm.     

CW Operation of a Submillimeter Wave Gyrotron (Gyrotron Fu IV) for High Stability of the Output Frequency

The first cw operation of our submillimeter wave gyrotron (Gyrotron FU IV) using a 12 T superconducting magnet has been successfully carried out. Output power is more than 20 W at a frequency of 301 GHz in the TE₀₃₁ resonant cavity mode. Time-resolved frequency measurement s shows that the frequency fluctuation of the gyrotron output is smaller than 2 MHz. This frequency fluctuation is mainly due to the fluctuation in the output voltage of the power supply.     

Recent results at LULI on fast electron transport with and without guiding cone in the context of fast ignitor

We present experimental and numerical results obtained at LULI (Laboratoire pour l’Utilisation des Lasers intenses) on propagation and energy deposition of laser-generated fast electrons into conical targets. The experimental measurements were performed by means of several diagnostics in order to assess the predicted benefit of conical targets over standard planar ones. Various configurations have been tried, regarding the laser parameters with the aim of optimizing the laser-to-target coupling. Our best results have been obtained when the laser was frequency-doubled at 0.53 μm, corresponding to interaction conditions without laser pedestal due to the ASE (Amplified Spontaneous Emission). Our data pinpoint the detrimental influence of the pre-plasma generated by the laser pedestal at 1.057 μm, whose confinement is enhanced in conical geometry as evidenced by shadowgraphic measurements which is also confirmed by 2D Cu-Ka transverse images obtained from Cu cones. The consequence is the filling of the cone, preventing the laser beam from efficiently reaching the cone tip. These experimental results are compared to 2D PIC simulations modeling of the laser-cone interaction.     

Electrical conductivity and local structure of lithium iron tungsten vanadate glass

A relationship between physical properties and local structure of 20Li₂O·10Fe₂O₃·xWO₃·(70–x)V₂O₅ glass, abbreviated as xLFWV glass (x?=?0???25 in mol%), was investigated by ⁵⁷Fe-Mössbauer spectroscopy, Fourier transform infrared spectroscopy (FT-IR), differential thermal analysis (DTA), leaching test using 20 vol% HCl and DC two- or four-probe method. ⁵⁷Fe-Mössbauer spectra of xLFWV glass showed an increase of quadrupole splitting (Δ) from 0.67 to 0.73_±0.02 mm s^???1 and a constant isomer shift (δ) of 0.39_±0.01 mm s^???1 with an increase of ‘x’ from 0 to 25. This suggests that Fe^IIIO₄ tetrahedra gradually increase their local distortion along with a substitution of WO₃ for V₂O₅. DTA of xLFWV glass showed an increase in glass transition temperature (T _g) from 252 to 298 $_{\pm 5}^{\circ}$ C with an increase of ‘x’. Composition dependency of T _g and Δ indicates that Fe^III atoms occupy substitutional sites of WO₆ octahedra as network former (NWF), since a large slope of 680 K (mm s^???1)^???1 was obtained in T _g ? Δ plot. Comparable electrical conductivities (σ) of 2.5 × 10^???6, 1.9 × 10^???6, 8.4 × 10^???7 and 2.9 × 10^???6 S cm^???1 obtained for xLFWV glasses with ‘x’ of 0, 10, 20 and 25, respectively increased to 2.4 × 10^???2, 2.4 × 10^???3, 3.5 × 10^???4 and 8.8 × 10^???5 S cm^???1 after annealing at 400 °C for 100 min. Smaller Δ values of 0.58 and 0.67_±0.02 mm s^???1 obtained in annealed xLFWV glasses with ‘x’ of 0 and 10, respectively indicate that structural relaxation occurs in VO₄ units of vanadate glass units, as had been observed in other vanadate glasses.