Dual Error Bounded Trajectory Simplification

2017 ◽  
Author(s):  
Xuelian Lin ◽  
Jiahao Jiang ◽  
Yimeng Zuo
Keyword(s):  
Bounded Trajectory

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

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Bo Gao ◽  
Xue-Mei Deng
Keyword(s):  
Magnetic Field ◽  
Black Holes ◽  
Monte Carlo ◽  
Charged Particles ◽  
Critical Energy ◽  
Periodic Oscillations ◽  
Test Particles ◽  
Charged Test ◽  
Twin Peak ◽  
Bounded Trajectory

AbstractWe 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.

Adaptive Control of Object Path Tracking and Finger Tip Slippage in a Multi-Fingered Robotic System

2008 ◽  
Author(s):  
Shahram Hadian Jazi ◽  
Mehdi Keshmiri ◽  
Farid Sheikholeslam
Keyword(s):  
Adaptive Control ◽  
System Dynamics ◽  
Trajectory Tracking ◽  
Adaptive Controller ◽  
Path Tracking ◽  
Control Synthesis ◽  
Parameter Uncertainties ◽  
New Approach ◽  
Finger Tip ◽  
Bounded Trajectory

Considering slippage between finger tips and an object, adaptive control synthesis of grasping and manipulating an object by a multi-fingered system is addressed in this paper. Slippage can occur due to many reasons such as disturbances, uncertainties in parameters and dynamics. In this paper, using a novel representation of friction and slippage dynamics, a new approach is introduced to analyze the system dynamics. Then an adaptive controller with a simple update rule is proposed to ensure the bounded trajectory tracking and slippage control, and at the same time to compensate for parameter uncertainties including coefficients of friction. The performance of the proposed adaptive controller is shown analytically and studied numerically.

scholarly journals BIFURCATION FROM ZERO OF A COMPLETE TRAJECTORY FOR NONAUTONOMOUS LOGISTIC PDES

2005 ◽  
Vol 15 (08) ◽  
pp. 2663-2669 ◽  
Author(s):  
JOSÉ A. LANGA ◽  
JAMES C. ROBINSON ◽  
ANTONIO SUÁREZ
Keyword(s):  
Bifurcation Theory ◽  
Simple Equation ◽  
First Eigenvalue ◽  
Logistic Equations ◽  
The First Eigenvalue ◽  
Nonautonomous Equation ◽  
Uniformly Bounded ◽  
Bounded Trajectory

In this paper we extend the well-known bifurcation theory for autonomous logistic equations to the nonautonomous equation [Formula: see text]0 < b0 < B0 < 2b0. In particular, we prove the existence of a unique uniformly bounded trajectory that bifurcates from zero as λ passes through the first eigenvalue of the Laplacian, which attracts all other trajectories. Although it is this relatively simple equation that we analyze in detail, other more involved models can be treated using similar techniques.

scholarly journals One-pass error bounded trajectory simplification

2017 ◽  
Vol 10 (7) ◽  
pp. 841-852 ◽  
Author(s):  
Xuelian Lin ◽  
Shuai Ma ◽  
Han Zhang ◽  
Tianyu Wo ◽  
Jinpeng Huai
Keyword(s):  
Bounded Trajectory

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

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Fu Yue-wen ◽  
Li Meng ◽  
Liang Jia-hong ◽  
Hu Xiao-qian
Keyword(s):  
Trajectory Planning ◽  
Computational Cost ◽  
Dynamic Environment ◽  
Crowd Simulation ◽  
Second Step ◽  
Pedestrian Navigation ◽  
The Third ◽  
Normal Individuals ◽  
Optimal Trajectory Planning ◽  
Bounded Trajectory

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.

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

2019 ◽  
Vol 150 (4) ◽  
pp. 2025-2054
Author(s):  
Piotr Kalita ◽  
Piotr Zgliczyński
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Dirichlet Boundary Conditions ◽  
Image Position ◽  
Space Interval ◽  
Bounded Trajectory

AbstractWe 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.

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