Aug 2026· Zenodo (CERN European Organization for Nuclear Research)
Abstract
This paper develops the economics of artificial intelligence as a single connected structure, from the physics of the production function to the aggregate growth constraint and the valuation of the firms building and adopting it. Part I derives the cost of capability from scaling laws, shows why deployed models are systematically overtrained, and estimates the task-success slope directly from 23,235 public evaluation runs: $\hat\beta=0.83$ with no detectable release-date trend. Part II treats market structure: minimum efficient scale, the two-tier equilibrium in which open weights contest the trailing edge but never the frontier, and inference as a capacity-constrained short-run market that rations rather than prices. Part III is the core. We replace the standard automation assignment rule with one that prices reliability, obtaining an automation calendar $t_{\mathrm{aut}}=t_{1/2}+(\tau/\beta)\log_2\gamma$ in which verification cost, not task difficulty, sets the date; derive optimal checkpoint spacing $k^\star\approx\sqrt{v_{\mathrm{ver}}/\lambda}$; and prove the exact best-of-$k$ result. Against a sound verifier, sampling divides the reliability lag by $k$ in the small-$k$ regime and does better outside it; against an unsound verifier, it leaves an error floor that no amount of sampling removes. Part IV aggregates: diffusion inherits its time dispersion from verification costs, and revenue growth is governed by the density of tasks at the current threshold. Part V proves a Baumol bound --- with elasticity of substitution below one, aggregate growth converges to that of the least automatable essential input --- and states three jointly necessary conditions for explosive growth. Part VI treats measurement, policy, and financial markets. Part VII states the investment bridge: technological importance, industry profit, and security return are distinct objects, and a coherent valuation must respect the automation calendar, rent migration, capital consumption, and expectations already in price. The full valuation architecture is reserved for a separate companion paper. Part VIII states eighteen open problems.
This paper describes the formulation of a numerical model for simulating environmentally driven one-dimensional (1D) ground movements of expansive clay. The formulation is based on a finite-element model that simulates the redistribution of matric suction through a diffusion-type equation, explicitly accounting for volume changes due to wetting and drying of the clay. We synthesize and modify highly nonlinear constitutive relationships for (1) hysteretic soil water retention; (2) reversible soil shrinkage and expansion of clay; and (3) hydraulic conductivity, explicitly incorporating desiccation cracks through a multidomain framework and assuming a critical surface crack depth. These models are well-calibrated to published laboratory tests on a reference expansive clay, Denver bentonite. We demonstrate capabilities of the proposed formulation to simulate the response of a homogeneous expansive clay to periods of drying and wetting, considering the initial matric suction, saturated hydraulic conductivity of the intact clay, and critical crack depth as three primary sources of uncertainty. We compare ensemble model simulations with measured ground movements from an instrumented expansive clay test site in Texas over a 3-year period using detailed records of potential evapotranspiration and precipitation. By assigning weights to the ensemble simulations based on their performance, we constrain the ranges of the three key uncertain parameters. The results showed very reasonable first-order agreement with the measured data and highlight the potential of the proposed formulation. We anticipate that more reliable predictions can be achieved through direct measurements of actual in situ evaporation rates and local soil properties.
Mahdi Seyyedan, Jiali Ma, Ivo Rosa Montenegro et al.· Journal of Geotechnical and...· 1 citation
A rational design for next-generation thermo-responsive nanocarriers is proposed, in which polymer chemistry, nanoparticle structure, experimental characterization, and mechanistic modelling are integrated from the earliest stages of material development.
M. Schifone, Giuseppe Nunziata, Filippo Rossi· Advances in Colloid and Inte...· 1 citation
Abstract The injection of CO 2 into geological reservoirs can acidify the reservoir environment, leading to the dissolution of mineral grains and increasing the risk of CO 2 leakage. A deeper understanding of these micro‐scale dissolution mechanisms is therefore essential for the safety of geological CO 2 sequestration. To address this challenge, we develop a multi‐field coupled simulation framework that integrates the Lattice Boltzmann Method (LBM) with the Finite‐Discrete Element Method (FDEM) to model solute transport and mineral micro‐structure dissolution. The framework incorporates a geometric mapping detection scheme and an improved momentum exchange algorithm to capture fluid‐solid interactions. Furthermore, a novel updating scheme for dissolution rates and solute concentrations is proposed, explicitly accounting for mass conservation and complex mineral morphology. A dynamic geometric topology updating algorithm is also proposed to track the morphological evolution of mineral grains. The accuracy and capability of the LBM‐FDEM framework are validated through several numerical benchmarks, including particle settling, solute release from a moving particle, dissolution of polymorphic particles, and reactive transport within a non‐uniform channel, yielding excellent agreement with existing solutions. Finally, this proposed method is applied to investigate the spatiotemporal evolution of fracture dissolution under varying Péclet numbers. The numerical results reveal that under diffusion‐dominated low Péclet regimes, product accumulation restricts dissolution to the upstream inlet, yielding a typical face dissolution pattern. Conversely, strong advection under high Péclet conditions drives rapid reactant penetration, triggering a uniform channelized widening along the entire fracture. Ultimately, this framework demonstrates significant potential for investigating complex hydro‐mechanical‐chemical couplings in subsurface engineering.
Zhijun Wu, Erkang Zhou, Xiang‐Yu Xu et al.· Water Resources Research· 0 citations
A new method for surgically removing training examples from a model reveals that as datasets grow, the link between what a model learns and what it produces dissolves.
