Since its first introduction, it has always been a subject of research to find models for a meaningful approximation of the highly accurate but complex Boltzmann equation. In the kinetic Fokker–Planck (FP) approach, a FP operator in velocity space is employed to approximate the collision integral of the Boltzmann equation. Instead of directly solving the resulting FP equation, a Monte Carlo technique is used to model an associated random process. This approach leads to an efficient stochastic solution algorithm. In recent years, the FP ansatz has become increasingly popular. Nevertheless, the modeling of gas mixtures in the context of kinetic FP has so far only been addressed in a very few papers. This article introduces a kinetic FP model that is capable of describing gas mixtures with particles interacting according to the hard-sphere collision model. The model is constructed to reproduce Grad’s 13 moment equations on a Navier–Stokes level of accuracy for gas mixtures with an arbitrary number of constituents. A stochastic simulation algorithm is derived that ensures a correct evolution of the species diffusion velocities and the species temperatures for a homogeneous gas, regardless of the applied time step size. It is shown that the proposed model is capable of correctly predicting shear stresses, heat fluxes, and diffusion velocities for different test cases, employing a He–Ar mixture.

Kinetic Fokker–Planck (FP) methods for modeling rarefied gas flows have received increasing attention over the last few years. However, formulating such models for realistic multi-species gases is still an open subject of research. Therefore, in this letter, we develop a kinetic FP model for describing gas mixtures with particles interacting according to the variable hard-sphere interaction potential. In accordance with the kinetic FP framework, a stochastic solution algorithm is employed in order to solve the model on a particle level. Different test cases are carried out, and the performance of the proposed method is compared with the direct simulation Monte Carlo algorithm.

Sealing MEMS devices by wafer capping is an important step during MEMS fabrication. Induced stress during capping may alter system behavior or may even reduce yield. Therefore, it is desirable for MEMS development and fabrication to have a technique to inspect and monitor dynamic behavior of mechanical structures in capped MEMS devices. MEMS gyroscopes in general are sensitive to stress introduced by the capping process because the resonances of mechanical structures have an influence to the sensor properties. In this paper we present the analysis of a MEMS gyroscope performed with an infrared confocal laservibrometer microscope. Vibration spectra and geometric parameters of capped MEMS structures are measured rapidly. We demonstrate that accurate vibration spectra can be obtained which we have utilized to analyze the influence of thermal loading in the capped device.

Chile’s livestock industry faces growing demands for emissions reduction, animal welfare, and value creation, while continuing to play a key role in rural food security and pasture-based production systems. In light of Chile’s varied agroclimatic conditions, a diminishing national herd, and shifting market signals, such as alternative proteins and distinctive meat products, this narrative review explores four complementary transition pathways: sustainable intensification, organic and agroecological systems, heritage livestock, and regenerative practices. We map the structural challenges, including grazing dairy and beef herds, fragmented producer organization, and the absence of unified, farm-scale greenhouse-gas measurements. We assess the management strategies that have the strongest support; viz., efficiency gains at the animal/herd level, adaptive grazing and silvopastoral designs, nutrient cycling via manure management and local by-products, and welfare frameworks that are aligned with national law and World Organisation for Animal Health guidance. Heritage systems (e.g., Chilota sheep breed in the Chiloé archipelago) provide resilience, cultural identity, and low-input baselines for stepwise transitions. Regenerative procedures can improve soil function and drought buffering but require context-specific designs and credible outcome-based verification to avoid greenwashing. Key enabling policies include coordinated certification and labeling covering animal welfare and origin. Additional elements are cooperative and territorial governance, targeted R&D and extension services for smallholders, and a transparent, standardized greenhouse-gas measurement framework linking farm-level actions to national inventories. Chile’s pathway is not a single model but a practical combination shaped by regional conditions that can deliver long-term economic sustainability, ecosystem services, and nutrition.