A Neural Network-Based Policy Iteration Algorithm with Global $$H^2$$ -Superlinear Convergence for Stochastic Games on Domains

In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear problem into a sequence of linear Dirichlet problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the \(H^2\)-norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo navigation problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.

     

Unsteady and chaotic characteristics of natural convection field in vertical slots at large Prandtl number

In this study we examined the unsteady and chaotic characteristics of the natural convection field in vertical slots at large Prandtl number. In the computation, temperature dependence of viscosity was partially taken into consideration. As a result we discovered that the spatial region where a significant temperature fluctuation is detected corresponds to the spatial region where the secondary cells exist. The largest Lyapunov exponents calculated from the temperature on the center line have a local maximum at the lower region of the enclosure when the viscosity change was considered. These characteristics agree well with the experimental ones that have been observed by authors (Ishida, Kure and Kimoto 2001).     

Substrates for flexible magnetic recording media: The role of base films for modern performance requirements

The trend in magnetic recording media is towards higher frequencies and larger storage capacities. Base film technology has developed in a manner analogous to corresponding demands on particulate and thin-film media, i.e. in the direction to reduced thickness, smoother surfaces, and very high uniformity. Key elements for the success of polyester films as substrates for all kinds of flexible media are new concepts for pigmentation and surface design. Future digital video recording systems and thin-film media will require new substrates with higher mechanical strength and thermal stability. Trends in base film development including dual-surface films and alternative polymer substrates are discussed.     

Study on crystalline properties of Er-Si-O compounds in relation to Er-related 1.54 μm photoluminescence and electrical properties

Er-Si-O crystalline compounds, which exhibit superlattice structures and sharp and strong Er-related 1.54 μm photoluminescence (PL) spectra at room temperature have been formed by self-assembling growth mechanism. Oxidation of the starting materials which have Si and Er at an atomic ratio of 2:1 are prepared and then oxidation and succeeding high-temperature annealing in Ar above 1250 °C cause a self-assembled superlattice-structured Er-Si-O crystalline compounds. The control of the ratio of Si and Er, as well as the following oxidation and annealing processes, is found to be sensitive to the crystalline properties, PL spectra and electrical properties. In this study, Er-Si-O crystalline thin films are formed on Si substrates by sol-gel and MOMBE methods, and their crystalline properties such as crystalline orientation and concentration ratio of Er, Si and O are investigated. Crystalline Er-Si-O films of high orientation are successfully grown on Si(1 0 0) and its inclined surface. The PL and excitation spectra, fluorescence decay and the electrical properties are found to be strongly related to the crystalline properties. Excess O causes a broader 1.54 μm PL spectra, slower fluorescence decay, lower carrier-mediated excitation and higher resistivity. A precise control of O is found to be necessary to grow superlattice-structured Er-Si-O compounds, which are semiconducting and are excitable via carrier-mediated excitation mechanism.     

Synthesis and refractive‐index control of fluoropolymers by the polyaddition of bis(epoxide)s and triazine di(aryl ether)s

The polyaddition of fluorine‐containing bis(epoxide)s and fluorine‐containing triazine di(aryl ether)s were examined to give the corresponding fluorine‐containing poly(cyanurate)s. It was observed that the synthesized fluoropolymers had good thermal stabilities and good film‐forming properties. The glass transition temperatures (T_g's) and refractive‐indices (n_D's) of synthesized polymers were determined by differential scanning calorimetry and ellipsometry, respectively, and it was found that the values of T_g's and n_D's were supported by their fluorine containing ratios and skeletons. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4421–4429, 2007     

Light Diffraction of Aligned Polymer Fibers Periodically Dispersed by Phase Separation of Liquid Crystal and Polymer

We have confirmed light diffraction of aligned polymer fibers obtained by a phase separation of an anisotropic-phase solution of liquid crystal and polymer. He—Ne laser light passing through the polymer fibers was scattered in the axis vertical to the fibers, and had two peaks of light intensity symmetrical to the center of the transmitting laser spot. The two peaks were found to be caused by light diffraction due to the periodic polymer-fiber dispersion because the peaks corresponded to values calculated by intervals between the fibers. The periodical fiber networks are considered to be formed by anisotropic spinodal decomposition. This effect can be used to measure the dispersion order of the polymer fibers. © 2004 The Optical Society of Japan     

Changes in the near-edge X-ray absorption fine structure spectra of long-chain diacetylene derivatives through photopolymerization in Langmuir–Blodgett films

Photopolymerization of cadmium 10,12-pentacosadiynoate (CdDA) in Langmuir–Blodgett (LB) films, with the molecular packing well arranged by moderate preannealing, was investigated with near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. Greenish films of polydiacetylene with an absorption wavelength of 705 nm were obtained through the photopolymerization of preannealed monomer LB films, and this resulted in an extended π-conjugate system based on the well-ordered monomer in a two-dimensional arrangement. The electronic structures of the polydiacetylenes were found to be correlated to the variation of the molecular arrangements in the films from the changes in the NEXAFS spectra through photopolymerization in the LB films. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2329–2336, 2004     

Linear and Nonlinear Optical Properties Of Racemic (±)2-(α-Methylbenzylamino)-5-Nitropyridine Single Crystals

Linear and nonlinear optical properties of racemic (±)2-(α-methylbenzylamino)-5-nitropyridine ((±)MBANP) single crystals have been comprehensively investigated and compared with those of the enantiomorph (–)2-(α-methylbenzylamino)-5-nitropyridine ((–)MBANP) crystals. (±)MBANP crystal exhibits very high chemical and physical stability, but relatively small nonlinear optical coefficients (d₃₁ = 6.8 pm/V, d₃₂ = 4.7 pm/V, d₃₃ = 0.84 pm/V). A comparison between the nonlinear optical coefficients of (±)MBANP and (–)MBANP demonstrates the validity of the oriented-gas model in molecular crystals that neglects all the contributions from intermolecular interaction.