Abstract Over the past three decades, evolutionary game theory in structured populations has witnessed explosive progress. Counterintuitive cooperative phenomena discovered in simulations have stimulated the development of rigorous mathematical theories to describe the underlying dynamics. In this paper, we review these theoretical advancements, including pair approximation and coalescent theory, which offer analytical solutions to evolutionary games on networks. We summarize the key results obtained by these theories, while also discussing their limitations, such as high computational complexity and constrained flexibility when applied to complex models. We therefore suggest that mathematical approaches provide a complementary tool for understanding cooperation in structured populations alongside simulations.
Abstract The prediction of acoustic radiation force (ARF) in biomedicine and materials science applications is crucial for the flexibility and precision of acoustic manipulation. Here, a theoretical model is established to describe the ARF on a liquid spheroidal particle in a cylindrical impedance cavity. An analytical expression for the ARF under a plane-wave irradiation is derived. The effects of the spheroidal materials, the fluid in the cavity and the aspect ratio of the particle on the ARF are analyzed. Results indicate that the particle materials significantly affect both the magnitude and resonant peaks of the ARF. By contrast, the surrounding fluid exerts a comparatively limited effect on the overall magnitude of the ARF, while substantially affecting the position of the resonant peaks. Moreover, as the spheroid becomes increasingly prolate, the magnitude of the ARF increases and the pronounced resonant peaks emerge. This study provides a theoretical guidance for the optimization of acoustic tweezers devices involving particle manipulation within an impedance cavity.
Abstract The present study provides theoretical insight into third harmonic generation (THG) in atomic clusters. Because atomic clusters are much smaller than the laser wavelength, their free electrons undergo collective oscillations under the action of the incident laser field. The restoring force acting on these electrons varies nonlinearly with the electron excursion, causing anharmonicity in the electron dynamics. Simultaneously, the ponderomotive force of the intense laser pulse perturbs the electron density within the cluster, generating a nonlinear current at the third harmonic frequency that is responsible for THG. Furthermore, laser irradiation causes the clusters to expand, forming a transient nanoplasma with time-dependent density and resonance conditions. The combination of anharmonic electron motion, efficient energy absorption, and broadened surface plasmon resonance significantly enhances the nonlinear current, leading to efficient harmonic generation. In this context, the present study focuses on optimizing the laser, cluster, and plasma parameters to maximize THG efficiency.
Abstract We introduce a novel quantum spin-glass model, a Sherrington-Kirkpatrick model with a transverse mean-field type random magnet. We rigorously derive the exact expression of the free energy of this model in the entire parameter region. The obtained exact solution implies the existence of a 1RSB-fullRSB transition at low temperatures. Our technique can be applied to general classical spin models, telling that any solvable classical spin model has its solvable quantum counterpart.
Abstract Methane hydrate nucleation in silica slit pores of 1–5 nm width is investigated by molecular dynamics simulations at temperatures between 250 and 295 K. Three-dimensional radial distribution functions reveal progressive suppression of hydrate-like structural order with decreasing pore width, with nucleation inhibited below a critical width between 2 and 3 nm. Projected two-dimensional radial distribution functions and spatially resolved F 3 and F 4 order parameter profiles show that, under strong confinement, pronounced in-plane organization persists while three-dimensional clathrate connectivity is absent. These structural descriptors provide a simple criterion for identifying the critical pore width below which hydrate nucleation is suppressed.
