Dynamics of charged test particles around quantum-corrected Schwarzschild black holes

We investigate neutral and charged test particles’ motions around quantum-corrected Schwarzschild black holes immersed in an external magnetic field. Taking the innermost stable circular orbits of neutral timelike particles into account, we find that the black holes can mimic different ranges of the Kerr black hole’s spin |a/M| from 0.15 to 0.99. Our analysis of charged test particles’ motions suggests that the values of the angular momentum l and the energy $$E^{2}$$ E 2 are slightly higher than Schwarzschild black holes. The allowed regions of the $$(l,E^{2})$$ ( l , E 2 ) demonstrate that the critical energy $$E^{2}_{c}$$ E c 2 divides the charged test particle’s bounded trajectory into three types. With the help of a Monte Carlo method, we study the charged particles’ probabilities of falling into the black holes and find that the probability density function against l depends on the signs of the particles’ charges. Finally, the epicyclic frequencies of the charged particles are considered with respect to the observed twin peak quasi-periodic oscillations frequencies. Our results might provide hints for distinguishing quantum-corrected Schwarzschild black holes from Schwarzschild ones by using the dynamics of charged test particles around the strong gravitational field.

Compact attractors of an antithetic integral feedback system have a simple structure

Since its introduction by Briat, Gupta and Khammash, the antithetic feedback controller design has attracted considerable attention in both theoretical and experimental systems biology. The case in which the plant is a two-dimensional linear system (making the closed-loop system a nonlinear four-dimensional system) has been analyzed in much detail. This system has a unique equilibrium but, depending on parameters, it may exhibit periodic orbits. An interesting open question is whether other dynamical behaviors, such as chaotic attractors, might be possible for some parameter choices. This note shows that, for any parameter choices, every bounded trajectory satisfies a Poincaré-Bendixson property. The analysis is based on the recently introduced notion of k-cooperative dynamical systems. It is shown that the model is a strongly 2-cooperative system, implying that the dynamics in the omega-limit set of any precompact solution is conjugate to the dynamics in a compact invariant subset of a two-dimensional Lipschitz dynamical system, thus precluding chaotic and other strange attractors.

On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions

We study the non-autonomously forced Burgers equation $$u_t(x,t) + u(x,t)u_x(x,t)-u_{xx}(x,t) = f(x,t)$$ on the space interval (0, 1) with two sets of the boundary conditions: the Dirichlet and periodic ones. For both situations we prove that there exists the unique H1 bounded trajectory of this equation defined for all t ∈ ℝ. Moreover we demonstrate that this trajectory attracts all trajectories both in pullback and forward sense. We also prove that for the Dirichlet case this attraction is exponential.

Optimal Acceleration-Velocity-Bounded Trajectory Planning in Dynamic Crowd Simulation

Creating complex and realistic crowd behaviors, such as pedestrian navigation behavior with dynamic obstacles, is a difficult and time consuming task. In this paper, we study one special type of crowd which is composed of urgent individuals, normal individuals, and normal groups. We use three steps to construct the crowd simulation in dynamic environment. The first one is that the urgent individuals move forward along a given path around dynamic obstacles and other crowd members. An optimal acceleration-velocity-bounded trajectory planning method is utilized to model their behaviors, which ensures that the durations of the generated trajectories are minimal and the urgent individuals are collision-free with dynamic obstacles (e.g., dynamic vehicles). In the second step, a pushing model is adopted to simulate the interactions between urgent members and normal ones, which ensures that the computational cost of the optimal trajectory planning is acceptable. The third step is obligated to imitate the interactions among normal members using collision avoidance behavior and flocking behavior. Various simulation results demonstrate that these three steps give realistic crowd phenomenon just like the real world.