scholarly journals Determinantal Expressions in Multi-Species TASEP

2020 ◽  
Author(s):  
Jeffrey Kuan ◽  
◽  
Keyword(s):  
Lattice Site ◽  
Large Time ◽  
Initial Conditions ◽  
Height Function ◽  
Fixed Time ◽  
Species Number ◽  
Homogeneous Case ◽  
Height Functions ◽  
Large Time Limit ◽  
Coalescing Random Walks

Consider an inhomogeneous multi-species TASEP with drift to the left, and define a height function which equals the maximum species number to the left of a lattice site. For each fixed time, the multi-point distributions of these height functions have a determinantal structure. In the homogeneous case and for certain initial conditions, the fluctuations of the height function converge to Gaussian random variables in the large-time limit. The proof utilizes a coupling between the multi-species TASEP and a coalescing random walk, and previously known results for coalescing random walks.

scholarly journals Fixed-Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Maoxing Liu ◽  
Jie Wu ◽  
Yong-zheng Sun
Keyword(s):  
Stability Analysis ◽  
Permanent Magnet ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Stability Control ◽  
Time Stability ◽  
Permanent Magnet Synchronous Motors ◽  
Synchronous Motors ◽  
Comparison Results

We firstly investigate the fixed-time stability analysis of uncertain permanent magnet synchronous motors with novel control. Compared with finite-time stability where the convergence rate relies on the initial permanent magnet synchronous motors state, the settling time of fixed-time stability can be adjusted to desired values regardless of initial conditions. Novel adaptive stability control strategy for the permanent magnet synchronous motors is proposed, with which we can stabilize permanent magnet synchronous motors within fixed time based on the Lyapunov stability theory. Finally, some simulation and comparison results are given to illustrate the validity of the theoretical results.

CAUSAL BULK VISCOUS COSMOLOGIES IN CONFORMALLY FLAT SPACETIME

2000 ◽  
Vol 09 (04) ◽  
pp. 475-493 ◽  
Author(s):  
M. K. MAK ◽  
T. HARKO
Keyword(s):  
Large Time ◽  
Viscosity Coefficient ◽  
Approximate Solutions ◽  
Conformally Flat ◽  
First Order ◽  
Flat Spacetime ◽  
Bulk Viscous ◽  
Type Differential Equation ◽  
Bulk Viscosity Coefficient ◽  
Large Time Limit

The evolution of a causal bulk viscous cosmological fluid filled open conformally flat spacetime is considered. By means of appropriate transformations the equation describing the dynamics and evolution of the very early Universe can be reduced to a first order Abel type differential equation. In the case of a bulk viscosity coefficient proportional to the square root of the density, ξ~ρ1/2, an exact and two particular approximate solutions are obtained. The resulting cosmologies start from a singular state and generally have a noninflationary behavior, the deceleration parameter tending, in the large time limit, to zero. The thermodynamic consistency of the results is also checked.

scholarly journals Large Deviations at Level 2.5 for Markovian Open Quantum Systems: Quantum Jumps and Quantum State Diffusion

2021 ◽  
Vol 184 (1) ◽  
Author(s):  
Federico Carollo ◽  
Juan P. Garrahan ◽  
Robert L. Jack
Keyword(s):  
Quantum State ◽  
Large Time ◽  
Stochastic Dynamics ◽  
Large Deviation ◽  
Open Quantum Systems ◽  
Photon Detection ◽  
State Diffusion ◽  
Quantum State Diffusion ◽  
Quantum Stochastic Processes ◽  
Large Time Limit

AbstractWe consider quantum stochastic processes and discuss a level 2.5 large deviation formalism providing an explicit and complete characterisation of fluctuations of time-averaged quantities, in the large-time limit. We analyse two classes of quantum stochastic dynamics, within this framework. The first class consists of the quantum jump trajectories related to photon detection; the second is quantum state diffusion related to homodyne detection. For both processes, we present the level 2.5 functional starting from the corresponding quantum stochastic Schrödinger equation and we discuss connections of these functionals to optimal control theory.

scholarly journals Optimal Control against the Human Papillomavirus: Protection versus Eradication of the Infection

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Fernando Saldaña ◽  
Andrei Korobeinikov ◽  
Ignacio Barradas
Keyword(s):  
Optimal Control ◽  
Human Papillomavirus ◽  
Control Problem ◽  
Initial Conditions ◽  
Fixed Time ◽  
Hpv Infection ◽  
Control Problems ◽  
Time Interval ◽  
Optimal Controls ◽  
Total Prevalence

We investigate the optimal vaccination and screening strategies to minimize human papillomavirus (HPV) associated morbidity and the interventions cost. We propose a two-sex compartmental model of HPV-infection with time-dependent controls (vaccination of adolescents, adults, and screening) which can act simultaneously. We formulate optimal control problems complementing our model with two different objective functionals. The first functional corresponds to the protection of the vulnerable group and the control problem consists of minimizing the cumulative level of infected females over a fixed time interval. The second functional aims to eliminate the infection, and, thus, the control problem consists of minimizing the total prevalence at the end of the time interval. We prove the existence of solutions for the control problems, characterize the optimal controls, and carry out numerical simulations using various initial conditions. The results and properties and drawbacks of the model are discussed.

Fixed-time trajectory tracking control for multiple nonholonomic mobile robots

2020 ◽  
pp. 014233122096641
Author(s):  
Meiying Ou ◽  
Haibin Sun ◽  
Zhenxing Zhang ◽  
Lingchun Li
Keyword(s):  
Mobile Robots ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
Initial Conditions ◽  
Fixed Time ◽  
Nonholonomic Mobile Robots ◽  
Trajectory Tracking Control ◽  
Adding A Power Integrator ◽  
Time Control ◽  
Power Integrator

This paper investigates the fixed-time trajectory tracking control for a group of nonholonomic mobile robots, where the desired trajectory is generated by a virtual leader, the leader’s information is available to only a subset of the followers, and the followers are assumed to have only local interaction. According to fixed-time control theory and adding a power integrator technique, distributed fixed-time tracking controllers are developed for each robot such that all states of each robot can reach the desired value in a fixed time. Moreover, the settling time is independent of the system initial conditions and only determined by the controller parameters. Simulation results illustrate and verify the effectiveness of the proposed schemes.

New fixed-time sliding mode control for a mismatched second-order system

2020 ◽  
pp. 014233122095230
Author(s):  
Guo Jianguo ◽  
Yang Shengjiang
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Nonlinear Function ◽  
Fixed Time ◽  
Second Order ◽  
Order System ◽  
Time Stability ◽  
Mode Control ◽  
Mismatched Uncertainties

A fixed-time sliding mode control (FTSMC) method is proposed for a second-order system with mismatched uncertainties in this paper. A new sliding mode, which is insensitive to the mismatched disturbance, is present to eliminate the effect of mismatched uncertainties by adopting the differentiable nonlinear function, and to obtain the fixed time stability independent of initial conditions by using the fraction-order function. In order to improve the performance of control system, the extended disturbance-observer-based fixed-time sliding mode control (EDO-FTSMC) approach is investigated to obtain the fixed-time stability subject to the mismatched uncertainties. Finally, the performance of the proposed control method is illustrated to compare other control approaches with numerical simulation results and application examples.

scholarly journals Energetics of Poisson–Kac Stochastic Processes Possessing Finite Propagation Velocity

2016 ◽  
Vol 41 (2) ◽  
Author(s):  
Antonio Brasiello ◽  
Massimiliano Giona ◽  
Silvestro Crescitelli
Keyword(s):  
Large Time ◽  
Coarse Grained ◽  
Langevin Equations ◽  
Stochastic Forcing ◽  
Stochastic Perturbations ◽  
Wiener Processes ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Almost Everywhere ◽  
Large Time Limit

AbstractA local fluctuation–dissipation theorem for the power delivered by a stochastic forcing is derived for Ornstein–Uhlenbeck processes driven by smooth, i. e. almost everywhere (a. e.)-differentiable stochastic perturbations (Poisson–Kac processes). An analytic expression for the probability density function of the fluctuational power is obtained in the large time limit. As these processes converge, in the Kac limit, toward classical Langevin equations driven by Wiener processes, a coarse-grained analysis of the statistical properties of the fluctuational work is developed.

scholarly journals Large-time limit of the quantum Zeno effect

2017 ◽  
Vol 58 (3) ◽  
pp. 032103 ◽  
Author(s):  
Paolo Facchi ◽  
Marilena Ligabò
Keyword(s):  
Large Time ◽  
Time Limit ◽  
Quantum Zeno Effect ◽  
Zeno Effect ◽  
Large Time Limit

On spacelike curves in hyperbolic space times sphere

2014 ◽  
Vol 11 (03) ◽  
pp. 1450014 ◽  
Author(s):  
Lingling Kong ◽  
Donghe Pei
Keyword(s):  
Hyperbolic Space ◽  
Height Function ◽  
Point Of View ◽  
De Sitter ◽  
Height Functions ◽  
Geometric Point

The main goal of this paper is to study singularities of lightlike surfaces and focal surfaces of spacelike curves in Hyperbolic space times sphere. To do that, we construct a de Sitter height function and a Lightcone height function, and then show the relation between singularities of the lightlike surfaces (respectively, the focal surfaces) and that of the de Sitter height functions (respectively, the Lightcone height functions). In addition, some geometry properties of the spacelike curves are studied from geometric point of view.

Experimental and theoretical investigation of an equation of dendritic crystal growth

1991 ◽  
Vol 2 (3) ◽  
pp. 199-222
Author(s):  
J. N. Dewynne ◽  
F. N. H. Robinson
Keyword(s):  
Harmonic Balance ◽  
Large Time ◽  
Multiple Scales ◽  
Initial Conditions ◽  
Dendritic Crystal ◽  
Method Of Harmonic Balance ◽  
Electronic Model ◽  
Wide Range ◽  
Periodic Form ◽  
Dissipative Terms

An experimental study using an analogue electronic model of the equation x‴ + x′ = є sin x, modified by the addition of small terms ax″ and βx with 0 < β < α ≫ є shows that these dissipative terms have a profound effect on the solutions for large time. If ∈ is not too large, experimental solutions tend to a simple periodic form, unlike the case α=β = 0. The existence of this limiting periodic form suggests the possibility of a simple analytic treatment using the method of harmonic balance, and this treatment leads to excellent agreement with the experimental results for a wide range of initial conditions and values of the parameters. The approach towards attracting limiting periodic solutions is analysed by using the method of multiple scales.

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