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Real‐time tracking of drug release from nanomedicine in vivo is crucial for optimizing its therapeutic efficacy in clinical settings, particularly in dosage control and determining the optimal therapeutic window. However, most current real‐time tracking systems require a tedious synthesis and purification process. Herein, a supramolecular nano‐tracker (SNT) capable of real‐time tracking of drug release in vivo based on non‐covalent host‐guest interactions is presented. By integrating multiple cavities into a single nanoparticle, SNT achieves co‐loading of drugs and probes while efficiently quenching the photophysical properties of the probe through host‐guest complexation. Moreover, SNT is readily degraded under hypoxic tumor tissues, leading to the simultaneous release of drugs and probes and the fluorescence recovery of probes. With this spatial and temporal consistency in drug loading and fluorescence quenching, as well as drug release and fluorescence recovery, SNT successfully achieves real‐time tracking of drug release in vivo (Pearson r = 0.9166, R2 = 0.8247). Furthermore, the released drugs can synergize effectively with fluorescent probes upon light irradiation, achieving potent chemo‐photodynamic combination therapy in 4T1‐bearing mice with a significantly improved survival rate (33%), providing a potential platform to significantly advance the development of nanomedicine and achieve optimal therapeutic effects in the clinic. [ABSTRACT FROM AUTHOR]

In this paper the Stokes system in an unbounded domain is solved by the artificial boundary method. The novelty lies in an operator form of the exact Dirichlet-to-Neumann (DtN) mapping. With the help of the Chebyshev rational approximation of the square root function, we derive a highly accurate approximate DtN mapping, which can be numerically implemented without resorting to the eigen-decomposition in terms of the vectorial spherical harmonics. In addition, we develop an efficient block preconditioner for the augmented truncated saddle point problem. Numerical experiments demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A second-order Crank-Nicolson finite difference method is designed to solve a 1D nonlocal Schrödinger equation on the whole real axis. We employ an asymptotically compatible scheme to discretize the spatially nonlocal operator, and apply the Crank-Nicolson scheme in time to achieve a fully discrete infinite system. An iterative technique for the second-order matrix difference equation is then developed to obtain Dirichlet-to-Dirichlet (DtD)-type artificial boundary conditions (ABCs) with the application of z-transform for the resulting fully discrete system. After that, with the aid of discrete nonlocal Green's first identity, we derive Dirichlet-to-Neumann (DtN)-type ABCs from DtD-type ABCs. The resulting DtN-type ABCs are available to reduce the infinite discrete system to a finite discrete system on a truncated computational domain, and make it possible to perform stability and convergence analysis for the reduced problem. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]