arXiv subjects

Jinqiao Duan

Publications and source records attributed to Jinqiao Duan.

269 records · Page 15Linked to original sources

arXiv2000

Averaging Principle for Quasi-Geostrophic Motions under Rapidly Oscillating Forcing

In this paper, the averaging principle for quasi-geostrophic motions with rapidly oscillating forcing is proved, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and attractor convergence are also investigated.

math.AP↗

arXiv1999

Almost Periodic Passive Tracer Dispersion

The authors investigate the impact of external sources on the pattern formation of concentration profiles of passive tracers in a two-dimensional shear flow. By using the pullback attractor technique for the associated nonautonomous dynamical system, it is shown that a unique time-almost periodic concentration profile exists for time-almost periodic external source.

chao-dyn↗

arXiv1999

Escape Probability and Mean Residence Time in Random Flows with Unsteady Drift

We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then develop numerical algorithms to solve for escape probability and mean residence time, which are described by backward Fokker-Planck type partial differential equations. A few computational issues are also discussed. Finally, we apply these ideas and numerical algorithms to a tidal flow model.

chao-dyn↗

arXiv1999

Dissipative Quasigeostrophic Motion under Temporally Almost Periodic Forcing

The full nonlinear dissipative quasigeostrophic model is shown to have a unique temporally almost periodic solution when the wind forcing is temporally almost periodic under suitable constraints on the spatial square-integral of the wind forcing and the $β$ parameter, Ekman number, viscosity and the domain size. The proof involves the pullback attractor for the associated nonautonomous dynamical system.

chao-dyn↗

arXiv1999

Chaotic Properties of Subshifts Generated by a Non-Periodic Recurrent Orbit

The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain non-periodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in metric spaces. These concepts include nonwandering point, recurrent point, eventually periodic point, scrambled set, sensitive dependence on initial conditions, Robinson chaos, and topological entropy. Next we review the notion of shift maps and subshifts. Then we show that the one-sided subshifts generated by a non-periodic recurrent point are chaotic in the sense of Robinson. Moreover, we show that such a subshift has an infinite scrambled set if it has a periodic point. Finally, we give some examples and discuss the topological entropy of these subshifts, and present two open problems on the dynamics of subshifts.

chao-dyn↗

arXiv1999

On the Stochastic Kuramoto-Sivashinsky Equation

In this article we study the solution of the Kuramoto-Sivashinsky equation (for surface erosion or surface growth) on a bounded interval subject to a random forcing term. We show that a unique solution to the equation exists for all time and depends continuously on the initial data.

math.DS↗

arXiv1999

Escape Probability, Mean Residence Time and Geophysical Fluid Particle Dynamics

Stochastic dynamical systems arise as models for fluid particle motion in geophysical flows with random velocity fields. Escape probability (from a fluid domain) and mean residence time (in a fluid domain) quantify fluid transport between flow regimes of different characteristic motion. We consider a quasigeostrophic meandering jet model with random perturbations. This jet is parameterized by the parameter $β= (2Ω)/r \cos (θ)$, where $Ω$ is the rotation rate of the earth, $r$ the earth's radius and $θ$ the latitude. Note that $Ω$ and $r$ are fixed, so $β$ is a monotonic decreasing function of the latitude. The unperturbed jet (for $0 < β< 2/3$) consists of a basic flow with attached eddies. With random perturbations, there is fluid exchange between regimes of different characteristic motion. We quantify the exchange by escape probability and mean residence time.

math.DS↗

arXiv1999

Nonlocal Dynamics of Passive Tracer Dispersion with Random Stopping

We investigate the nonlocal behavior of passive tracer dispersion with random stopping at various sites in fluids. This kind of dispersion processes is modeled by an integral partial differential equation, i.e., an advection-diffusion equation with a memory term. We have shown the exponential decay of the passive tracer concentration, under suitable conditions for the velocity field and the probability distribution of random stopping time.

math.DS↗

arXiv1998

Asymptotic Dynamical Difference between the Nonlocal and Local Swift-Hohenberg Models

In this paper the difference in the asymptotic dynamics between the nonlocal and local two-dimensional Swift-Hohenberg models is investigated. It is shown that the bounds for the dimensions of the global attractors for the nonlocal and local Swift-Hohenberg models differ by an absolute constant, which depends only on the Rayleigh number, and upper and lower bounds of the kernel of the nonlocal nonlinearity. Even when this kernel of the nonlocal operator is a constant function, the dimension bounds of the global attractors still differ by an absolute constant depending on the Rayleigh number.

math.DS↗

arXiv1998

Dynamics of a Nonlocal Kuramoto-Sivashinsky Equation

In this paper we study the effects of a ``nonlocal'' term on the global dynamics of the Kuramoto-Sivashinsky equation. We show that the equation possesses a ``family of maximal attractors'' parameterized by the mean value of the initial data. The dimension of the attractor is estimated as a function of the coefficient of the nonlocal term and the width of the periodic domain.

math.DS↗

arXiv1998

Trajectory and Attractor Convergence for a Nonlocal Kuramoto-Sivashinsky Equation

The nonlocal Kuramoto-Sivashinsky equation arises in the modeling of the flow of a thin film of viscous liquid falling down an inclined plane, subject to an applied electric field. In this paper, the authors show that, as the coefficient of the nonlocal integral term goes to zero, the solution trajectories and the maximal attractor of the nonlocal Kuramoto-Sivashinsky equation converge to those of the usual Kuramoto-Sivashinsky equation.

math.DS↗

arXiv1998

A Remark on the Three Dimensional Baroclinic Quasigeostrophic Dynamics

We consider time-periodic patterns of the dissipative three dimensional baroclinic quasigeostrophic model in spherical coordinates, under time-dependent forcing. We show that when the forcing is time-periodic and the spatial square-integral of the forcing is bounded in time, the model has time-periodic solutions.

math.DS↗

arXiv1998

Passive Tracer Dispersion with Random or Periodic Source

In this paper, the author investigates the impact of external sources on the pattern formation and long-time behavior of concentration profiles of passive tracers in a two-dimensional shear flow. It is shown that a time-periodic concentration profile exists for time-periodic external source, while for random source, the distribution functions of all concentration profiles weakly converge to a unique invariant measure (like a stationary state in deterministic systems) as time goes to infinity

chao-dyn↗

arXiv1998

Infinite-Dimensional Linear Dynamical Systems with Chaoticity

The authors present two results on infinite-dimensional linear dynamical systems with chaoticity. One is about the chaoticity of the backward shift map in the space of infinite sequences on a general Fréchet space. The other is about the chaoticity of a translation map in the space of real continuous functions. The chaos is shown in the senses of both Li-Yorke and Wiggins. Treating dimensions as freedoms, the two results imply that in the case of an infinite number of freedoms, a system may exhibit complexity even when the action is linear. Finally, the authors discuss physical applications of infinite-dimensional linear chaotic dynamical systems.

chao-dyn↗

arXiv1998

On a Linear Chaotic Quantum Harmonic Oscillator

We show that a linear quantum harmonic oscillator is chaotic in the sense of Li-Yorke. We also prove that the weighted backward shift map, used as an infinite dimensional linear chaos model, in a separable Hilbert space is chaotic in the sense of Li-Yorke, in addition to being chaotic in the sense of Devaney.

chao-dyn↗

arXiv1998

Time-Periodic Quasigeostrophic Motion under Dissipation and Forcing

The quasigeostrophic equation is a prototypical geophysical fluid model. In this paper, we consider time-periodic motions of this model under dissipation and time-dependent wind forcing. We show that when the wind forcing is time-periodic and the spatial square-integral of the wind forcing is bounded in time, the full nonlinear quasigeostrophic model has time-periodic motions, under some conditions on $β$ parameter, Ekman number, viscousity and the domain size.

math.DS↗

arXiv1998

Dissipative Quasigeostrophic Dynamics under Random Forcing

The quasigeostrophic model is a simplified geophysical fluid model at asymptotically high rotation rate or at small Rossby number. We consider the quasigeostrophic equation with dissipation under random forcing in bounded domains. We show that global unique solutions exist for appropriate initial data. Unlike the deterministic quasigeostrophic equation whose well-posedness is well-known, there seems no rigorous result on global existence and uniqueness of the randomly forced quasigeostrophic equation. Our work provides such a rigorous result on global existence and uniqueness, under very mild conditions.

math.DS↗