Geometric Analysis of Non-Linear Diffusion Processes

Modeling Environmentally Driven Seasonal Moisture Migration and Ground Movements in Expansive Clays

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.

Modelling the impact of temperature on nanocarrier behavior: Thermodynamics, structural transitions, and drug release.

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.

Data augmentation for intelligent fault diagnosis based on feature pre-extraction mechanism and improved conditional denoising diffusion probabilistic models under data scarcity

Conditional denoising diffusion model for missing value imputation in smart meter data

Generative Artificial Intelligence and Diffusion models in Drug Discovery: A Critical Review

The Economics of Artificial Intelligence: Scaling, Verification, Assignment, Capital, Growth, and Value

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.