41 Result(s)

Article

Inverse Problem of the Thermoelastic Plate System with a Curved Middle Surface and Memory Term

This paper is concerned with an inverse problem of a coupled thermoelastic plate model. Two major features are that the thermal equation has a memory effect, while the plate equation has a curved middle surfac...

Song-Ren Fu, Liangbiao Chen, Goong Chen, Peng-Fei Yao in The Journal of Geometric Analysis (2024)

Article

Animal Shapes, Modal Analysis, and Visualization of Motion (IV): Geometric Constructions and Implementation

We address computer implementation and technology issues in geometric constructions for mathematical and computational modeling purposes, especially regarding 3D finite-element mesh generation for large scale ...

**g Yang, Goong Chen, Chunqiu Wei, Alexey Sergeev… in The Journal of Geometric Analysis (2023)

Article

Animal Shapes, Modal Analysis, and Visualization of Motion (I): Horse and Camel

Eigenfunctions and eigenvalues of physical systems and engineering structures can reveal many of the system’s fundamental features and, therefore, become a basis for the study of inverse problems. In this seri...

Goong Chen, **gtong Huang, Chunqiu Wei, **g Yang… in The Journal of Geometric Analysis (2023)

Article

Animal Shapes, Modal Analysis, and Visualization of Motion (III): Giraffe, Duck, Goose, T-Rex Dinosaur, and the Flying Modes of Eagle

This paper contains more varieties of animals, including the giraffe, bird species duck, goose and eagle, and the T-Rex dinosaur. They range across mammals, birds and reptiles. For each of them, we present the...

**g Yang, Goong Chen, Chunqiu Wei, Alexey Sergeev… in The Journal of Geometric Analysis (2023)

Article

Animal Shapes, Modal Analysis, and Visualization of Motion (II): Dynamics and Fourier Decomposition

This paper begins with solving the linear elastodynamic equation with forcing by expanding it into Fourier series. We then proceed to prove the conservation laws of momentum, angular momentum, and energy. We i...

Goong Chen, Chunqiu Wei, Alexey Sergeev, **g Yang… in The Journal of Geometric Analysis (2023)

Article

Boundary controllability of structural acoustic systems with variable coefficients and curved walls

This paper studies a structural acoustic model consisting of an interior acoustic wave equation with variable coefficients and a coupled Kirchhoff plate equation with a curved middle surface. By the Riemannian...

Fengyan Yang, Pengfei Yao, Goong Chen in Mathematics of Control, Signals, and Systems (2018)

Article

The virial theorem and ground state energy estimates of nonlinear Schrödinger equations in \(\mathbb {R}^2\) with square root and saturable nonlinearities in nonlinear optics

The virial theorem is a nice property for the linear Schrödinger equation in atomic and molecular physics as it gives an elegant ratio between the kinetic and potential energies and is useful in assessing the ...

Tai-Chia Lin, Milivoj R. Belić… in Calculus of Variations and Partial Differe… (2017)

Article

Concentration Problems for Bandpass Filters in Communication Theory over Disjoint Frequency Intervals and Numerical Solutions

The concentration problem of maximizing signal strength of bandlimited and timelimited nature is important in communication theory. In this paper we consider two types of concentration problems for the signals...

Indranil SenGupta, Bo Sun, Weisheng Jiang… in Journal of Fourier Analysis and Applicatio… (2012)

Chapter

Total Variations of Iterates of Maps

Goong Chen, Yu Huang in Chaotic Maps (2011)

Chapter

Bifurcation Theorems for Maps

Bifurcation means “branching “. It is a major nonlinear phenomenon. Bifurcation happens when one or several important system parameters change values in a transition process. After a bifurcation, the system’s ...

Goong Chen, Yu Huang in Chaotic Maps (2011)

Chapter

Fractals

We begin this chapter by giving some simple constructions.

Goong Chen, Yu Huang in Chaotic Maps (2011)

Chapter

Infinite-dimensional Systems Induced by Continuous-Time Difference Equations

Goong Chen, Yu Huang in Chaotic Maps (2011)

Chapter

Simple Interval Maps and Their Iterations

The discovery of many nonlinear phenomena and their study by systematic methods are a major breakthrough in science and mathematics of the 20th Century, leading to the research and development of nonlinear scienc...

Goong Chen, Yu Huang in Chaotic Maps (2011)

Chapter

Ordering among Periods: The Sharkovski Theorem

One of the most beautiful theorems in the theory of dynamical systems is the Sharkovski Theorem. An interval map may have many different periodic points with seemingly unrelated periodicities. What is unexpect...

Goong Chen, Yu Huang in Chaotic Maps (2011)

Chapter

Homoclinicity. Lyapunoff Exponents

Goong Chen, Yu Huang in Chaotic Maps (2011)

Chapter

The Smale Horseshoe

The Smale horseshoe offers a model for pervasive high-dimensional nonlinear phenomena, as well as a powerful technique for proving chaos. Here in this chapter, we present the famous Smale horseshoe and show th...

Goong Chen, Yu Huang in Chaotic Maps (2011)

Chapter

Rapid Fluctuations of Chaotic Maps on ℝ^N

We have studied in Chapter 2 the use of total variations to characterize the chaotic behavior of interval maps. In this chapter, we will generalize such an approach to maps on multi-dimensional spaces.

Goong Chen, Yu Huang in Chaotic Maps (2011)

Chapter

Symbolic Dynamics, Conjugacy and Shift Invariant Sets

Goong Chen, Yu Huang in Chaotic Maps (2011)