• CNT alignment can be tailored inside the liquid matrix by external electric fields. • Composites have higher electrical conductivity and lower percolation threshold. • A CNT polarization kinetic model and a homogenization scheme are built. • A coated-CNT model is built to analyze frequency-dependent interfacial effects. • Three independent experimental validation confirms the model's accuracy. Carbon nanotube (CNT)-based nanocomposites exhibit exceptional electrical tunability under external electric fields, while the dynamics of field-driven CNT alignment and its impact on transverse isotropy of the overall composite remain underexplored. This study establishes a unified micro-mesoscale framework to decode the electro-structural evolution of CNT-polymer composites. We integrate an overdamped rotational kinetics model for CNT reorientation with an effective-medium homogenization scheme, incorporating interfacial electron tunneling, electron hopping, and dielectric relaxation. Our theory quantifies how electric field parameters (strength, frequency, and duration) govern CNT alignment-characterized by a maximum distribution angle-and subsequently modulate the composite's effective electrical conductivity and dielectric permittivity. Validated against three independent experiments, this work provides insights into the alignment dynamics of CNTs, the evolution of percolation thresholds, and the field-tuned electrical behaviors of composites. The modeling and theory are crucial for the design and optimization of CNT nanocomposites for flexible electronics, energy storage, and field-responsive smart materials.

• Modelling commitment in a two-stage optional Prisoner’s Dilemma game. • Optionality boosts commitment but fails to sustain cooperation, leading to exit. • A strict rule boosts cooperation by closing an ‘opportunistic exit’ loophole. • Flexible rules may yield higher social welfare when exit options are beneficial. • Guides the institutional design to maximise both cooperation and social welfare. Commitment is a well-established mechanism for fostering cooperation in human society and multi-agent systems, while most research on commitment-based cooperation assumes compulsory participation. This overlooks many real-world scenarios where individuals are free to abstain from an interaction. We address this gap by proposing a two-stage evolutionary game model that integrates commitment with the optional Prisoner’s Dilemma. In our model, players first decide whether to commit and then choose to cooperate, defect, or exit. We find that optional participation boosts commitment acceptance but fails to foster cooperation, leading instead to widespread exit behaviour. To address this, we compare two institutional incentives: a strict rule rewarding only committed cooperators, and a flexible rule rewarding any committed non-defector. Results show that the strict rule is better for promoting cooperation, as the flexible rule creates a loophole for opportunistic exits. However, the flexible rule can yield higher social welfare when exit options are highly beneficial. Our study highlights the need for well-designed incentives in voluntary settings to effectively promote both cooperation and social welfare.

• A simple hybrid gravity source term is proposed for viscoplastic thin-layer models • The hybrid term incorporates both topographic slope and surface height gradients • Improves prediction of front positions and free-surface profiles in dam-break flows • Demonstrates better agreement with experiments than classical slope-based models • Applicable to both lubrication and shallow water equations across slope regimes The ability of thin-layer models to produce physically correct flow solutions in the acceleration, deceleration, and stopping phase is very crucial for industrial and geophysical applications. In this work, we propose a simple hybrid approximation of the gravity source term for the lubrication approximation and the shallow water equations, aimed at preventing the overestimation of front positions in dam-break-type flows. The proposed formulation incorporates contributions from both the topographic slope and the free-surface height gradients, offering a more balanced representation of gravitational forcing across different regions of the flow domain. This is particularly important for yield stress fluids, whose motion depends on gravity-induced stresses exceeding a critical yield threshold. The proposed model allows better prediction of the free-surface profile in the tip and rear regions for both shallow and steep inclinations. We observe excellent agreements with experiments compared to existing numerical solutions in the literature, which rely solely on classical slope-driven gravity terms.