Tao Guo

We study massive point particles with intrinsic random motion and no inserted pair force. Instead of erasing local counting statistics in an unstructured field sample, we retain a fixed physical representative volume and resolve its occupation sectors. Maxwell speed and von Mises–Fisher direction statistics determine the local velocity moments. An explicit Eulerian constitutive bridge transfers the suppressed center fluctuation of an occupied group to conservative carrier exchange between neighboring representative elements. For an arbitrary occupation law, the sum over all nonempty sectors then collapses to the void probability and yields a general anisotropic density–reduced-momentum system. Instantaneous Poisson occupation, a common centered activity mobility factor, and integrated isotropy select a deterministic nonlinear two-field equation. Thus microscopic randomness and structured occupation generate an effective collective transport coupling without a microscopic pair potential, collision operator, or external stochastic force. Two applications of the same operator exhibit a conditional compensated Newton-shaped longitudinal response and a boundary-flux-supported stationary branch with simultaneous azimuthal circulation and axial current. These sectors do not establish a universal gravitational constant or a source-free, three-dimensionally stable jet.

Eugenol (Eug) holds potential as a treatment for bacterial rhinosinusitis by nasal powder drug delivery. To stabilization and solidification of volatile Eu

The spread of upper respiratory tract (URT) infections harms people’s health and causes social burdens. Developing targeted treatment strategies for URT infections that exhibit good biocompatibility, stability, and strong antimicrobial effects remains challenging. The dual antimicrobial and antiviral effects of iodine (I₂) in combination with the cooling sensation of l-menthol in the respiratory tract can simultaneously alleviate URT inflammation symptoms. However, as both I₂ and l-menthol are volatile, addressing stability issues is crucial. In this study, a potassium iodide β-cyclodextrin metal–organic framework [β-CD-POF(I)] with appropriate particle size was used to coload and deliver I₂ and l-menthol. Primarily, β-CD-POF(I) was employed as the most efficient carrier to significantly enhance the stability of I₂, surpassing any other known protection strategies in the pharmaceutical field (CD complexations, PVP conjugations, and cadexomer iodine). The mechanism underlying the improvement in stability of I₂ by β-CD-POF(I) was investigated through scanning electron microscopy with energy-dispersive X-ray spectroscopy, X-ray photoelectron spectroscopy, Raman spectroscopy, and molecular docking. The results revealed that the key processes involved in improving stability were the inclusion of I₂ by β-CD cavities in β-CD-POF(I) and the formation of polyiodide anion between iodine ions and I₂. Furthermore, the potential of β-CD-POF(I) to load and deliver drugs was validated, and coloading of l-menthol and I₂ demonstrated reliable stability. β-CD-POF(I) achieved a rate of URT deposition ≥95% in vitro, and the combined antibacterial effects of coloaded I₂ and l-menthol was better than I₂ or PVP-I alone, with no irritation noted following URT administration in rabbits. Therefore, the stable coloading of drugs by β-CD-POF(I), leading to enhanced antimicrobial effects, provides a new strategy for treating URT infections.

In this study, we investigate the behavior of randomly moving particles with a defined average energy, focusing on their biased motion around a specific point. These particles' velocity magnitudes follow a Maxwell distribution with a specific scale parameter. Our analysis derives the stochastic rotation rules for these particles and introduces the Ito equation conditions for biased stochastic rotation at a given curl value. We also consider the special relativistic-like effects in this context. The findings are validated through a representative example.

In a particle swarm with a fixed kinetic energy, the constituent particles move randomly and their velocity magnitudes follow a Maxwell distribution characterized by specific parameters. Within a certain time frame, particles in a sub-swarm may exhibit a bias in their movement direction. Thus, the particles may exhibit a special characteristic (biased random motion), where the group velocity in a particular direction remains constant u. For this biased particle swarm, composed of randomly moving particles with a fixed average speed c, particles have a higher probability of moving in a specific direction. Conversely, their likelihood of moving in all other directions is equally reduced. This study starts from the perspective of biased random walks and using Mathematica software proves that the diffusion rate of particles (in the reference frame R_u observed from R₀) in all directions is slower than that of an unbiased particle swarm with the same average speed c. Specifically, the degree of reduction is determined by the Lorentz-like factor. Lastly, we present the Ito equation for this biased random motion and provide associated verification examples. This study aims to serve as a reference for comprehending the underlying principles of the special relativity effect.

Cyclodextrin metal-organic frameworks (CD-MOFs) exhibit a high structural diversity, which contributes to their functional properties. In this study, we ha

Essential oil (EO) is widely used in the pharmaceutical, cosmetic, agriculture, and food industries because of its aromatic, antioxidant, and antibacterial properties. However, the weak interactions caused by small contact area with various substrates pose significant challenges to experimental detection and molecular simulation. In this study, the main components and contents of compound essential oil (CEO) were determined by gas chromatography-mass spectrometry (GC-MS) and gas chromatography (GC), respectively. As a result, 11 components were screened out from CEO and their contents were measured. And synthetic essential oil (SEO) was deployed as a simplified CEO model for subsequent research according to the above result. In addition, a porous cyclodextrin metal-organic framework (CD-MOF) was used to load SEO, and the detailed process of experimental determination and molecular simulation prediction of the content of volatile oil components in CD-MOF was shown. The results of experiments and molecular simulations have consistently proved that CD-MOF had a selective absorption effect on SEO components. Furthermore, the interaction mechanism and release characteristics of these components in CD-MOF were investigated. The results of the release kinetics analysis provided references for the identification of the diffusion type of each component. In conclusion, the strategies established in this article provide ideas for the experimental detection and molecular simulation of multi-component competitive existence in carriers under weak interactions.

The protection of unstable anticancer molecules and their delivery to lesions are challenging issues in cancer treatment. Topotecan (TPT), a classic cytotoxic drug, is widely used for treating refractory lung cancer. However, the therapeutic effects of TPT are jeopardized by its active lactone form that is intrinsically hydrolyzed in physiological fluids, resulting in low bioavailability. Herein, the TPT-loaded crosslinked cyclodextrin metal-organic framework (TPT@CL-MOF) was engineered to improve the local bioavailability of TPT for the treatment of lung cancer. CL-MOF exhibited the efficient loading (12.3 wt%) of TPT with sustained release characteristics. In particular the formulation offered excellent protection in vitro against hydrolysis and increased the half-life of TPT from approximately 0.93 h to 22.05 h, which can be attributed to the host–guest interaction between cyclodextrin and TPT, as confirmed by molecular docking. The TPT@CL-MOF could effectively kill the cancer cells and inhibit the migration and invasion of B16F10 cells in vitro. Moreover, TPT@CL-MOF was efficiently distributed in the lungs after intravenous administration. In an in vivo study using a B16F10 pulmonary metastatic tumor model, TPT@CL-MOF significantly reduced the number and size of metastatic lung nodules at a reduced low dose by five times, and no noticeable side effects were observed. Therefore, this study provides a possible alternative therapy for the treatment of lung cancer with the camptothecin family drugs or other unstable therapeutically significant molecules.