Test of conformal gravity with astrophysical observations

Since it can describe the rotation curves of galaxies without dark matter and can give rise to accelerated expansion, conformal gravity attracts much attention recently. As a theory of modified gravity, it is important to test conformal gravity with astrophysical observations. Here we constrain conformal gravity with SNIa and Hubble parameter data and investigate whether it suffers from an age problem with the age of APM~08279+5255. We find conformal gravity can accommodate the age of APM~08279+5255 at 3 $\sigma$ deviation, unlike most of dark energy models which suffer from an age problem.Comment: 6 pages, 2 figure

Traveling Wave in a Ratio-dependent Holling-Tanner System with Nonlocal Diffusion and Strong Allee Effect

In this paper, a ratio-dependent Holling-Tanner system with nonlocal diffusion is taken into account, where the prey is subject to a strong Allee effect. To be special, by applying Schauder's fixed point theorem and iterative technique, we provide a general theory on the existence of traveling waves for such system. Then appropriate upper and lower solutions and a novel sequence, similar to squeeze method, are constructed to demonstrate the existence of traveling waves for c>c*. Moreover, the existence of traveling wave for c=c* is also established by spreading speed theory and comparison principle. Finally, the nonexistence of traveling waves for c<c* is investigated, and the minimal wave speed then is determined

A sufficient condition on successful invasion by the predator

In this paper, we provide a sufficient condition on successful invasion by the predator. Specially, we obtain the persistence of traveling wave solutions of predator-prey system, in which the predator can survive without the predation of the prey. This proof heavily depends on comparison principle of scalar monostable equation, the rescaling method and phase-plane analysis

Traveling Waves of Modified Leslie-Gower Predator-prey Systems

The spreading phenomena in modified Leslie-Gower reaction-diffusion predator-prey systems are the topic of this paper. We mainly study the existence of two different types of traveling waves. Be specific, with the aid of the upper and lower solutions method, we establish the existence of traveling wave connecting the prey-present state and the coexistence state or the prey-present state and the prey-free state by constructing different and appropriate Lyapunov functions. Moreover, for traveling wave connecting the prey-present state and the prey-free state, we gain more monotonicity information on wave profile based on the asymptotic behavior at negative infinite. Finally, our results are applied to modified Leslie-Gower system with Holling II type or Lotka-Volterra type, and then a novel Lyapunov function is constructed for the latter, which further enhances our results. Meanwhile, some numerical simulations are carried to support our results

Quantification of the influence of drugs on zebrafish larvae swimming kinematics and energetics

The use of zebrafish larvae has aroused wide interest in the medical field for its potential role in the development of new therapies. The larvae grow extremely quickly and the embryos are nearly transparent which allows easy examination of its internal structures using fluorescent imaging techniques. Medical treatment of zebrafish larvae can directly influence its swimming behaviours. These behaviour changes are related to functional changes of central nervous system and transformations of the zebrafish body such as muscle mechanical power and force variation, which cannot be measured directly by pure experiment observation. To quantify the influence of drugs on zebrafish larvae swimming behaviours and energetics, we have developed a novel methodology to exploit intravital changes based on observed zebrafish locomotion. Specifically, by using an in-house MATLAB code to process the recorded live zebrafish swimming video, the kinematic locomotion equation of a 3D zebrafish larvae was obtained, and a customised Computational Fluid Dynamics tool was used to solve the fluid flow around the fish model which was geometrically the same as experimentally tested zebrafish. The developed methodology was firstly verified against experiment, and further applied to quantify the fish internal body force, torque and power consumption associated with a group of normal zebrafish larvae vs. those immersed in acetic acid and two neuroactive drugs. As indicated by our results, zebrafish larvae immersed in 0.01% acetic acid display approximately 30% higher hydrodynamic power and 10% higher cost of transport than control group. In addition, 500 μM diphenylhydantoin significantly decreases the locomotion activity for approximately 50% lower hydrodynamic power, whereas 100 mg/L yohimbine has not caused any significant influences on 5 dpf zebrafish larvae locomotion. The approach has potential to evaluate the influence of drugs on the aquatic animal’s behaviour changes and thus support the development of new analgesic and neuroactive drugs