Search

We introduce a random barrier to a supercritical branching random walk in an i.i.d. random environment $\{\mathcal{L}_n\}$ indexed by time $n,$ i.e., in each generation, only the individuals born below the barrier can survive and reproduce. At generation $n$ ($n\in\mathbb{N}$), the barrier is set as $\chi_n+\varepsilon n,$ where $\{\chi_n\}$ is a random walk determined by the random environment. Lv \& Hong (2024) showed that for almost every $\mathcal{L}:=\{\mathcal{L}_n\},$ the quenched survival probability (denoted by $\varrho_{\mathcal{L}}(\varepsilon)$) of the particles system will be 0 (resp., positive) when $\varepsilon\leq 0$ (resp., $\varepsilon>0$). In the present paper, we prove that $\sqrt{\varepsilon}\log\varrho_\mathcal{L}(\varepsilon)$ will converge in Probability/ almost surely/ in $L^p$ to an explicit negative constant (depending on the environment) as $\varepsilon\downarrow 0$ under some integrability conditions respectively. This result extends the scope of the result of Gantert et al. (2011) to the random environment case.

Consider a supercritical branching random walk in a time-inhomogeneous random environment. We impose a selection (called barrier) on survival in the following way. The position of the barrier may depend on the generation and the environment. %to indexed by time $n,$ i.e.,$\{\L_n\}$with a random absorption barrier In each generation, only the individuals born below the barrier can survive and reproduce. When the barrier causes the extinction of the system, we give the extinction rate in the sense of $L^p~(p\geq 1)$. Moreover, we show the $L^p$ convergence of the small deviation probability for a random walk with random environment in time., Comment: 26 Pages

To investigate the 1.6 GeV high-energy proton beam detector utilized in the CSNS Phase-II upgrade project, a plastic scintillator detector presents a viable option due to its superior radiation hardness. This study investigates the effects of irradiation damage on a BC408 plastic scintillator induced by 80 MeV protons, including absorption and fluorescence spectroscopy, and light yield tests of BC408 pre- and post-proton irradiation, with a focus on determining the radiation resistance threshold of BC408. The results indicate that the performance of BC408 remains unimpaired at absorbed doses up to 5.14*10^3 Gy/cm3, demonstrating its ability to absorb 1.63*10^13 p/cm3 1.6 GeV protons while maintaining stability. This suggests that BC408 could potentially be used as the 1.6 GeV high-energy proton beam detector in the CSNS Phase-II upgrade project.

Consider the invariance principle for a random walk with random environment (denoted by $\mu$) in time on $\bfR$ in a weak quenched sense. We show that a sequence of the random probability measures on $\bfR$ generated by a bounded Lipschitz functional $f$ and $\mu$ will converge in distribution to another random probability measures, which is related to $f$ and two independent Brownian motions. The upper bound of the convergence rate has been obtained. We also explain that in general, this convergence can not be strengthened to the almost surely sense., Comment: 13 pages, 0 figures

We consider a supercritical branching random walk in time-inhomogeneous random environment with a random absorption barrier, i.e.,in each generation, only the individuals born below the barrier can survive and reproduce. Assume that the random environment is i.i.d..The barrier is set as $\chi_n+an^{\alpha},$ where $a,\alpha$ are two constants and $\{\chi_n\}$ is a certain i.i.d. random walk determined by the random environment.We show that for almost surely given environment (i.e., a sequence of point processes which is a realization of the random environment), the time-inhomogeneous branching random walk under the given environment will become extinct (resp., survive with positive probability) if $\alpha<1/3$ or $\alpha=1/3, a1/3, a>0$ or $\alpha=1/3, a>a_c$), where $a_c$ is a positive constant determined by the random environment. The rates of extinction when $\alpha<\frac{1}{3}, a\geq0$ and $\alpha=1/3, a\in(0,a_c)$ are also obtained. These extend the main results in A\"{\i}d\'{e}kon $\&$ Jaffuel (2011) and Jaffuel (2012),to the random environment case. The influence caused by the random environment have been specified.

We consider the small deviation probability for random walk with time-inhomogeneous random environment. Compared with the result in Mogul'ski\u{\i} (1974) for the i.i.d. random walk, the rate is smaller (due to the random environment), which is specified in terms of the quenched and annealed variance., Comment: 21 pages, 0 figures

Objective: Interstitial fluid flow through vascular adventitia has been disclosed recently. However, its kinetic pattern was unclear. Methods and Results: We used histological and topographical identifications to observe ISF flow along venous vessels in rabbits. By MRI in alive subjects, the inherent ISF flow pathways in legs, abdomen and thorax were enhanced by paramagnetic contrast from ankle dermis. By fluorescence stereomicroscopy and layer-by-layer dissection after the rabbits were sacrificed, the perivascular and adventitial connective tissues (PACT) along the saphenous veins and inferior vena cava were found to be stained by sodium fluorescein from ankle dermis, which coincided with the findings by MRI. By confocal microscopy and histological analysis, the stained PACT pathways were verified to be the fibrous connective tissues and consisted of longitudinally assembled fibers. By usages of nanoparticles and surfactants, a PACT pathway was found to be accessible for a nanoparticle under 100nm and contain two parts: a tunica channel part and an absorptive part. In real-time observations, the calculated velocity of a continuous ISF flow along fibers of a PACT pathway was 3.6-15.6 mm/sec. Conclusion: These data further revealed more kinetic features of a continuous ISF flow along vascular vessel. A multiscale, multilayer, and multiform interstitial/interfacial fluid flow throughout perivascular and adventitial connective tissues was suggested as one of kinetic and dynamic mechanisms for ISF flow, which might be another principal fluid dynamic pattern besides convective/vascular and diffusive transport in biological system., Comment: 28 pages, 8 figures