diffusion models

Fast adsorption of Mn2+ and Zn2+ on commercial LTA zeolite: kinetics, equilibrium, and preliminary reuse assessment

Abstract Commercial LTA-type zeolite was evaluated for the adsorption of Mn 2+ and Zn 2+ from aqueous solutions, with emphasis on the relationship between framework properties and adsorption behavior. Despite its very low BET surface area, the zeolite showed rapid and highly efficient uptake of both metal ions, reaching near-equilibrium within the first minute. Kinetic modeling indicated site-controlled adsorption consistent with pseudo-second-order behavior, while equilibrium data were described by the Langmuir model, confirming monolayer adsorption on uniform exchange sites. Intraparticle diffusion played a secondary role, and Zn 2+ exhibited faster site occupation than Mn 2+ . Stoichiometric analysis of Na + release during adsorption, together with blank experiments, demonstrated that metal uptake occurs mainly through Na + /divalent ion exchange within the zeolite framework, with partial release of loosely bound sodium. This ion-exchange mechanism explains the high adsorption capacities obtained despite the very low external surface area, since performance is governed by framework charge density rather than surface adsorption. Germination assays with Cucumis sativus showed no acute phytotoxic effects for metal-loaded zeolites, indicating potential for safe reuse as a micronutrient source. These results demonstrate that commercial LTA zeolite enables fast and efficient metal removal and provide a proof-of-concept for sustainable post-adsorption valorization of the spent material.

Can the low-altitude economy promote high-quality agricultural development? From the perspective of factor mobility

The low-altitude economy, characterized by high-tech support, efficient operations, and high-quality development, has become a new engine for cultivating new quality productive forces in agriculture and accelerating the modernization of agriculture and rural areas. Based on the Chinese government’s new development philosophy, this study constructs a comprehensive index of high-quality agricultural development. Using panel data for 31 provinces in China from 2004 to 2024, this study employs a difference-in-differences model and a mediation-effect model to empirically examine the impact of the low-altitude economy on high-quality agricultural development. The results show that the low-altitude economy significantly promotes high-quality agricultural development. Further analysis indicates that the low-altitude economy indirectly drives high-quality agricultural development by promoting technology diffusion and labor mobility. Among the mediating channels, technology diffusion has the strongest mediating effect, while the coefficient of the mediating effect of capital flow is positive but statistically insignificant. The promotion effect of the low-altitude economy on high-quality agricultural development is more pronounced in major grain-consuming areas, eastern and central regions, and regions with higher levels of digital infrastructure. Accordingly, this study proposes policy recommendations in terms of rationally arranging agricultural low-altitude application scenarios, facilitating factor mobility, and implementing differentiated regional development paths for the low-altitude economy. These findings provide empirical references for relevant departments to scientifically formulate low-altitude economic development plans and promote high-quality agricultural development.

Future-Sufficient Control Quotients Robust Closure, Operational Reduction, and Physical Realization

A task-relative theory of what may be forgotten, what may be ignored in practice, and what need not be physically maintained Reduced representations can be sufficient in at least three inequivalent senses: they may close under a declared family of future continuations, support near-optimal decisions for a specified objective, or admit economical physical realization. We formalize these as structural, operational, and physical future sufficiency. For finite-horizon controlled Markov systems, exact quotient conditions yield Bellman factorization. In finite-dimensional linear systems, backward propagation of task observables gives the minimal robust future-relevance family, with a continuous-time moving-null criterion characterizing exact closure. For finite-horizon linear-quadratic regulation, we define a strong closure residual, construct a nearby exactly closed surrogate problem, and obtain a local quadratic policy-regret certificate. A controlled perturbation experiment reproduces the predicted first-order gain deviation and second-order regret scaling. Exact counterexamples and a diffusion-control comparison show that strong closure is nevertheless not necessary for near-optimal control: performance-oriented reductions can tolerate substantial structural nonclosure and attain much smaller operational order. We then distinguish reduced control dimension from physical realization burden. Effective-support and mobility bounds show that low operational rank need not imply localized or inexpensive implementation, while a Clifford-circuit construction exhibits rank-one observable relevance with extensive Pauli support. The resulting framework treats closure as a robustness guarantee rather than a universal compression optimum and identifies the additional assumptions required to convert informational reduction into physical resource advantage. Keywords: future sufficiency; controlled quotients; model reduction; optimal control; LQR; state aggregation; bisimulation; physical realization; quantum control; coheroputation Scope and claim discipline This paper does not claim that task-oriented model reduction, state aggregation, bisimulation, balanced truncation, reduced Riccati control, observable backpropagation, or a posteriori reduced-control certification are new. Those are mature areas with substantial prior art [3–13]. The contribution is narrower: the paper places robust structural closure, task-performance sufficiency, and hardware-relative physical sufficiency in one explicit hierarchy; develops a particular strong-closure residual and exactly closed surrogate for finite-horizon LQR; and proves no-go separations showing why reduced informational dimension alone cannot be promoted to a physical resource claim.

A multi-phase hygro-mechanical phase-field model for drying shrinkage of concrete

TorchEBM: A Composable PyTorch Library for Energy-Based and Transport-Based Generative Models

TorchEBM is a PyTorch library for generative models defined either by a scalar potential or by a transport between densities. Energy-based models, diffusion, flow matching, and Schrödinger bridges are factored into one set of composable primitives: energies and fields, interpolants, couplings, training objectives, samplers, and numerical integrators. Simulation-free objectives such as flow matching, equilibrium matching, and denoising score matching require no sampling in the training loop; sampling-based objectives such as contrastive divergence remain available where a calibrated energy is needed.

Molecular Dynamics Simulations of Ion Transport in Ionophilic Nanopores — Neutral and Charged Systems

This dataset contains all input files, simulation results, and a master data table from molecular dynamics (MD) simulations of ion transport in electrolyte-filled slit nanopores, performed with GROMACS version 2024.2. Both charge-neutral and surface-charged pore systems are included. The associated publication is: "Interfacial adsorption and field-assisted hopping govern ion conductivity in electrolyte-filled nanopores" Simulation Input Files GROMACS input files necessary to reproduce the simulations are provided for both neutral and charged pore systems. The surface–ion interaction strength (ionophilicity) is controlled through the Lennard-Jones parameters in ffnonbonded.itp, which can be varied across eight values for the neutral case and two representative values (low and high ionophilicity) for the charged case. For the charged systems, the surface charge density is defined in ffnonbonded.itp and in the topology files CG_bot_charged.itp and CG_top_charged.itp, which specify the charge distribution on the bottom and top pore walls, respectively. Initial configuration files and run parameter files (grompp.mdp) are provided for all systems. Master Data Table A CSV file (simulation_master_table.csv) is included in which each row corresponds to a single simulation and columns specify the pore width, ionophilicity parameters, surface charge density, applied electric field, system composition, and all key extracted results (ionic current, Green–Kubo conductivity, ion-pairing correlation factor, diffusion coefficients, and adsorption free energies). This file provides a complete mapping between simulation parameters and results. Simulation Results — Neutral Pores Results are provided across five pore widths (H = 0.9, 1.9, 2.6, 4.8, and 9.2 nm) and eight ionophilicity values: Ionic current under applied electric fields of 0.0–1.0 V/nm, with block-averaging standard errors, extracted via the Helfand moment method. Green–Kubo conductivity (σ_GK), Nernst–Einstein conductivity (σ_NE), cross-correlation conductivity (σ_cross), and the ion-pairing correlation factor (β), computed from zero-field equilibrium simulations. In-plane diffusion coefficients for Na⁺ and Cl⁻ from mean-squared displacement analysis at zero electric field. Adsorption free energies (ΔG_min) for Na⁺ and Cl⁻ from Boltzmann inversion of the equilibrium density profiles. Simulation Results — Charged Pores Results are provided for three pore widths (H = 1.9, 4.8, and 9.2 nm), four surface charge densities (Σ_s = 0.5, 1.0, 1.5, and 2.0 e/nm²), and two ionophilicity values: Total, interfacial, and pore-center ionic currents under applied electric fields of 0.0–1.0 V/nm, with block-averaging standard errors. Simulation Protocols All simulations used the Nosé–Hoover thermostat at 300 K with a relaxation constant of 1.0 ps and the SPC/E water model. Electrolyte concentration was 1 M NaCl. For full details of the simulation protocols, theoretical framework, and analysis methods, please refer to the associated publication. If further clarification is needed, please contact the corresponding author: Mohammad Javad Abdolhosseini Qomi — mjaq@uci.edu

Traveling Waves in a Diffusive Single-Species Model with a Weak Spatiotemporal Memory Kernel

We study traveling wave solutions in a nonlinear reaction-diffusion model incorporating a weak spatiotemporal distributed memory kernel. The model describes a single-species population whose movement is influenced by both random diffusion and memory-based dispersal, with the latter expressed as a convolution term involving a temporal weighting function and a spatial Green’s function. This framework captures the gradual decay of spatial memory and its effect on dispersal dynamics. Using perturbation expansions, operator theory, and the Banach fixed-point theorem, we establish the existence of traveling wavefronts connecting equilibrium states in two parameter regimes: (i) a small memory-based diffusion coefficient and (ii) a large wave speed. The analysis addresses significant challenges arising from the nonlocal, nonlinear memory term by employing integral equation representations and precise estimates. Numerical simulations illustrate how the memory diffusion coefficient and mean delay influence wave speed, front shape, and population distribution. The results provide a rigorous characterization of wave propagation in systems with weak distributed memory, offering a unified approach applicable to models in population dynamics, biological invasion, and other spatiotemporal processes with memory effects.

Studie van de impact van thermische gradiënten op de betrouwbaarheid van metalen gebruikt in de micro-elektronica

The continuous scaling of microelectronic technologies has made back-end-of-line (BEOL) interconnect reliability increasingly sensitive to non-uniform thermal conditions. Reduced interconnect dimensions, high current densities, Joule heating, and nearby heat sources can generate pronounced temperature gradients along metal lines. Under such conditions, temperature is no longer merely a scalar parameter controlling diffusion kinetics: its spatial gradient introduces an additional driving force for atomic transport, known as thermomigration (TM). The resulting mass transport can interact with electromigration (EM) and stress migration (SM), thereby modifying void nucleation, void growth, and ultimately interconnect lifetime. This PhD investigates the impact of thermal gradients on the reliability of metal interconnects, with a particular focus on Cu interconnects. Experimental studies are combined with finite-element simulations and analytical modelling to quantify temperature distributions, thermally driven atomic transport, and the resulting reliability degradation. Dedicated test structures are used to investigate TM-induced void formation and growth under controlled non-uniform temperature fields. Analytical and numerical models are developed to describe TM-driven mass transport and to predict critical regions for void nucleation and growth. The interaction of TM with other driving forces, particularly EM and mechanically induced stress gradients, is also investigated to establish a more complete description of atomic flux under realistic operating conditions. The developed framework further enables lifetime estimation under combined electrical and thermal loading. The results demonstrate that sufficiently strong and non-uniform temperature distributions can significantly alter interconnect degradation and, under relevant conditions, make TM an important contributor to reliability failure. This work provides a physics-based framework for assessing interconnect reliability in the presence of thermal gradients and supports more accurate lifetime prediction for advanced microelectronic technologies.

Application Of Fractional Calculus in Modeling and Reducing Road Accidents

Abstract Traditional mathematical models of traffic flow and driver behavior rely on integer-order calculus, which assumes localized, instantaneous changes. However, real-world traffic systems exhibit strong memory effects, non-local interactions, and anomalous diffusion. This paper explores the application of fractional calculus utilizing non-integer orders in reducing road accidents. By integrating fractional derivatives into traffic flow dynamics, viscoelastic tire-road friction models, and advanced driver assistance systems (ADAS), we demonstrate how capturing hereditary properties can optimize highway design, vehicular control, and active safety systems to actively prevent collisions.

Application Of Fractional Calculus in Modeling and Reducing Road Accidents

Abstract Traditional mathematical models of traffic flow and driver behavior rely on integer-order calculus, which assumes localized, instantaneous changes. However, real-world traffic systems exhibit strong memory effects, non-local interactions, and anomalous diffusion. This paper explores the application of fractional calculus utilizing non-integer orders in reducing road accidents. By integrating fractional derivatives into traffic flow dynamics, viscoelastic tire-road friction models, and advanced driver assistance systems (ADAS), we demonstrate how capturing hereditary properties can optimize highway design, vehicular control, and active safety systems to actively prevent collisions.

Accelerating Materials Discovery: A Review of Machine Learning in X‐Ray Absorption Spectroscopy

X‐ray absorption spectroscopy (XAS) is a critical technique for probing the local structural and electronic properties of materials. Advanced synchrotron radiation facilities generate complex, high‐dimensional spectra, which pose significant challenges for traditional analysis methods while simultaneously offering unprecedented opportunities for machine learning (ML). This review systematically elaborates how ML models are driving the transformation of XAS data analysis. We not only cover supervised and unsupervised learning methods for spectral classification and clustering but also delve into cutting‐edge deep learning architectures. These include graph neural networks for precise “structure‐to‐spectra” mapping and diffusion models for generative tasks and structure prediction. We provide a comprehensive overview of the key challenges in data‐driven XAS, including the feature engineering of spectra and structures, strategies for solving the “spectra‐to‐structure” Inverse Problem, and Sim2Real methods for bridging the “Domain Gap” between simulated and experimental data. Furthermore, we emphasize the importance of model eXplainable artificial intelligence and uncertainty quantification for building trust in scientific research. Finally, this review looks ahead to the future of the field, driven by materials informatics and autonomous experiments. Active Learning techniques, represented by Bayesian optimization, are pioneering “self‐driving” smart XAS experiments, which will greatly accelerate the discovery and design of new materials.

The Cognitive Familiarity Supremacy Theory (CFST)

The Cognitive Familiarity Supremacy Theory (CFST) proposes that a substantial portion of human certainty, ideological attachment, collective identity formation, and perceived superiority emerges not primarily from objective rational evaluation, but from repeated familiarity encoding mechanisms operating within subconscious cognitive architectures.This framework argues that repeated environmental exposure, social conditioning, emotional reinforcement, identity fusion, symbolic repetition, and institutional amplification collectively construct familiarity-driven epistemic structures that are frequently mistaken for objective truth, rational certainty, or universal superiority. The theory synthesizes and mathematically formalizes principles from cognitive neuroscience, psychology, sociology, political theory, philosophy of mind, epistemology, systems theory, information theory, complexity science, behavioral economics, evolutionary biology, communication studies, artificial intelligence, anthropology, cybernetics, and cultural theory into a unified explanatory framework.CFST introduces a comprehensive causal chain model:Repeated Exposure \rightarrow Subconscious Encoding \rightarrow Identity Fusion \rightarrow Emotional Reinforcement \rightarrow Bias Formation \rightarrow Perceived Superiority.The theory proposes that human cognition operates through familiarity-weighted interpretive systems, where the subjective sensation of certainty often emerges from accumulated familiarity intensity rather than objective verification.The framework further integrates: Bayesian epistemology, predictive processing, Hebbian learning, social identity theory, information entropy, network propagation, algorithmic amplification, memetic evolution, cultural conditioning, political hegemony, and neurocognitive attractor-state dynamics.The theory also develops: formal mathematical models, belief topology equations, dynamic systems formulations, stochastic familiarity propagation systems, agent-based ideological simulations, network-theoretical belief diffusion structures, and computational cognitive equilibrium equations.At the civilizational level, CFST proposes that societies are partially constructed upon collectively reinforced familiarity architectures rather than purely objective truth systems. At the individual level, it explains ideological rigidity, nationalism, fanaticism, cultural supremacy perception, identity-protective cognition, and epistemic polarization.Finally, the theory proposes that genuine epistemic liberation requires conscious disruption of subconscious familiarity monopolies through critical reasoning, diversity exposure, meta-cognitive awareness, and reflective epistemological reconstruction.