东京大学

The Kullback–Leibler divergence together with exponential families establishes the foundation of information geometry and is widely generalized. Among the generalization, we focus on the (h,τ)-divergence and (h,τ)-exponential families. We present a sufficient condition for the (h,τ)-divergence to induce a Hessian structure on an (h,τ)-exponential family. We also define the (h,τ)-dependence of random variables and prove a kind of the law of large numbers.

Accelerated corrosion tests qualify protective coatings for steel bridges, yet their quantitative correspondence to field exposure is poorly established, especially for localized degradation at coating defects. We use 3D laser profilometry to quantify coating blistering over time and the terminal substrate corrosion of defective painted steel in four environments, comprising two field sites (Choshi, Pacific-coast; Miyakojima, subtropical marine) and two accelerated tests (ISO 16539 Method B and a composite cyclic test), for four coating systems. The acceleration factor (accelerated/field blister volume at comparable exposure) is large (≈13–200×), strongly coating-dependent, and site-dependent; the composite cyclic test far exceeds ISO 16539, and both greatly exceed the field. The coating ranking is preserved across environments, but accelerated tests inflate the spread between best and worst coatings, so a single acceleration factor cannot serve for quantitative life prediction. Cumulative time-of-wetness only weakly explains field degradation, and the two sites do not share a common dose–response curve; adding measured airborne sea-salt (≈1.8× higher at Miyakojima) as a second driver improves the fit and explains much of the inter-site difference. By contrast, the non-destructive blister volume predicts the post-blast substrate corrosion through a single transferable power law (corrosion volume is proportional to blister volume^0.60, R2 = 0.89; corrosion depth, R2 = 0.80) holding across all environments and the three coatings with measurable corrosion. The blister–corrosion mechanism is thus consistent across the environments studied though the rate is not, giving a non-destructive basis for estimating hidden corrosion beneath intact coatings and a foundation for data-driven cross-environment prediction.

We consider a two-component semilinear reaction-diffusion system in a bounded spatial domain Ω over a time interval (0,T), which governs the water density u(x,t) and the vegetation biomass density v(x,t) for x and 0<t<T. In this system, called the Klausmeier-Gray-Scott model, we assume that an unknown source depends only on the spatial variable and appears in the reaction-diffusion equation for u. The main subject is the inverse source problem of determining a source term from limited data on (u,v). We establish two kinds of stability estimates by means of Carleman estimates. First, a Carleman estimate with a singular weight yields a Lipschitz stability estimate for the inverse source problem from data consisting of a snapshot u(·,t_0) in Ω and (u,v) in a subdomain ω over a time interval. Second, without assuming boundary data, we prove a Hölder stability estimate in any interior subdomain Ω_0 satisfying Ω_0. We further study how much the observation data can be reduced while preserving uniqueness and stability in the inverse problem under suitable additional conditions.

A three-dimensional numerical model is developed to predict the electrochemical performance of polymer electrolyte fuel cell cathodes using catalyst-layer microstructures reconstructed from focused ion beam scanning electron microscopy images. Proton conduction, gas diffusion, and electrochemical reactions are solved using the lattice Boltzmann method (LBM). To reduce the computational cost while retaining local microstructural information, an anisotropic sub-grid scale (SGS) model is introduced. In this model, direction-dependent effective diffusivities and conductivities are evaluated from the reconstructed microstructures and assigned to each coarse computational cell, allowing the coarse-grid simulation to retain the local anisotropic transport characteristics of the catalyst layer. The model is validated under various operating conditions. The calculated cathode overpotentials agree well with the experimental results, with errors of less than 8%. The overpotential breakdown also shows physically reasonable trends. The validated model is then applied to cathodes with different ionomer distributions. The results show that increasing the ionomer content near the membrane side improves cathode performance. This trend is further confirmed by experiments using double-layer cathode electrodes. The proposed framework provides a practical method for connecting microstructural information with cathode performance prediction, which can support future catalyst layer design.

The greenhouse gas sequestration capacity of forests is an important pillar in combating global warming; therefore establishing a forest resource circulation system is crucial. Forestry, which includes everything from cultivation to harvesting forests that store carbon dioxide as they grow, and the sawmill industry, which processes this timber, frequently face significant economic challenges. Consequently, proposals are needed to establish systems that improve these industries’ economic competitiveness while also ensuring the forest resources circulation. This study developed a model to evaluate the economic relationship between timber processing and energy consumption from a sector-coupling perspective using a prospective techno-economic analysis. It specifically defines wood utilization as a comprehensive forest resource circulation that includes production, planting, processing, energy utilization, and reforestation. It evaluates the economic interdependence between timber processing and energy utilization when all wood is harvested from forests and both uses are combined. The evaluation results show that combining energy utilization in sawmills processing over 36,000 m3 annually allows for full harvesting from forests, reducing forest residues, and lowering site preparation costs for reforestation. Additionally, using inexpensive electricity from biomass power generation for sawmilling lowers sawmill costs. It has become clear that, at sawmills of a certain size or larger, combining material utilization with energy utilization results in a slight decrease in sawmilling costs, while reducing forestry management costs; overall, this is an effective approach for wood utilization.