Global Existence and Asymptotic Behavior of Solutions to a Chemotaxis-Fluid System on General Bounded Domain

In this paper, we investigate an initial-boundary value problem for a chemotaxis-fluid system in a general bounded regular domain $\Omega \subset \mathbb{R}^N$ ($N\in\{2,3\}$), not necessarily being convex. Thanks to the elementary lemma given by Mizoguchi & Souplet [10], we can derive a new type of entropy-energy estimate, which enables us to prove the following: (1) for $N=2$, there exists a unique global classical solution to the full chemotaxis-Navier-Stokes system, which converges to a constant steady state $(n_\infty, 0,0)$ as $t\to+\infty$, and (2) for $N=3$, the existence of a global weak solution to the simplified chemotaxis-Stokes system. Our results generalize the recent work due to Winkler [15,16], in which the domain $\Omega$ is essentially assumed to be convex

Well-posedness and long-time behavior of a non-autonomous Cahn-Hilliard-Darcy system with mass source modeling tumor growth

In this paper, we study an initial boundary value problem of the Cahn-Hilliard-Darcy system with a non-autonomous mass source term $S$ that models tumor growth. We first prove the existence of global weak solutions as well as the existence of unique local strong solutions in both 2D and 3D. Then we investigate the qualitative behavior of solutions in details when the spatial dimension is two. More precisely, we prove that the strong solution exists globally and it defines a closed dynamical process. Then we establish the existence of a minimal pullback attractor for translated bounded mass source $S$. Finally, when $S$ is assumed to be asymptotically autonomous, we demonstrate that any global weak/strong solution converges to a single steady state as $t\to+\infty$. An estimate on the convergence rate is also given

Container Terminal Berth-Quay Crane Capacity Planning Based on Markov Chain

This paper constructs a berth-quay crane capacity planning model with the lowest average daily cost in the container terminal, and analyzes the influence of the number of berths and quay cranes on the terminal operation. The object of berth-quay crane capacity planning is to optimize the number of berths and quay cranes to maximize the benefits of the container terminal. A steady state probability transfer model based on Markov chain for container terminal is constructed by the historical time series of the queuing process. The current minimum time operation principle (MTOP) strategy is proposed to correct the state transition probability of the Markov chain due to the characteristics of the quay crane movement to change the service capacity of a single berth. The solution error is reduced from 7.03% to 0.65% compared to the queuing theory without considering the quay crane movement, which provides a basis for the accurate solution of the berth-quay crane capacity planning model. The proposed berth-quay crane capacity planning model is validated by two container terminal examples, and the results show that the model can greatly guide the container terminal berth-quay crane planning

The localization of single pulse in VLBI observation

In our previous work, we propose a cross spectrum based method to extract single pulse signals from RFI contaminated data, which is originated from geodetic VLBI postprocessing. This method fully utilizes fringe phase information of the cross spectrum and hence maximizes signal power, however the localization was not discussed in that work yet. As the continuation of that work, in this paper, we further study how to localize single pulses using astrometric solving method. Assuming that the burst is a point source, we derive the burst position by solving a set of linear equations given the relation between residual delay and offset to a priori position. We find that the single pulse localization results given by both astrometric solving and radio imaging are consistent within 3 sigma level. Therefore we claim that it is possible to derive the position of a single pulse with reasonable precision based on only 3 or even 2 baselines with 4 milliseconds integration. The combination of cross spectrum based detection and the localization proposed in this work then provide a thorough solution for searching single pulse in VLBI observation. According to our calculation, our pipeline gives comparable accuracy as radio imaging pipeline. Moreover, the computational cost of our pipeline is much smaller, which makes it more practical for FRB search in regular VLBI observation. The pipeline is now publicly available and we name it as "VOLKS", which is the acronym of "VLBI Observation for frb Localization Keen Searcher".Comment: 11 pages, 4 figures, 3 tables, accepted for publication in A

Assessing the Therapeutic Effect of 630 nm Light-emitting Diodes Irradiation on the Recovery of Exercise-induced Hand Muscle Fatigue with Surface Electromyogram

This paper aims to investigate the effect of light emitting diode therapy (LEDT) on exercise-induced hand muscle fatigue by measuring the surface electromyography (sEMG) of flexor digitorum superficialis. Ten healthy volunteers were randomly placed in the equal sized LEDT group and control group. All subjects performed a sustained fatiguing isometric contraction with the combination of four fingertips except thumb at 30% of maximal voluntary contraction (MVC) until exhaustion. The active LEDT or an identical passive rest therapy was then applied to flexor digitorum superficialis. Each subject was required to perform a re-fatigue task immediately after therapy which was the same as the pre-fatigue task. Average rectified value (ARV) and fractal dimension (FD) of sEMG were calculated. ARV and FD were significantly different between active LEDT and passive rest groups at 20%–50%, 70%–80%, and 100% of normalized contraction time (P \u3c 0.05 ). Compared to passive rest, active LEDT induced significantly smaller increase in ARV values and decrease in FD values, which shows that LEDT is effective on the recovery of muscle fatigue. Our preliminary results also suggest that ARV and FD are potential replacements of biochemical markers to assess the effects of LEDT on muscle fatigue