What is Chaos? A mathematician discussing chaos is featured in the movie Jurassic Park. James Gleick's book Chaos remains on the best-seller list for many months. The characters of Tom Stoppard's celebrated p l ayArcad i a discourse on the meaning of chaos. What is the fuss about? Chaos is a new science that establishes the omnipresence of unpredictability as a fundamental feature of common exp...

In this paper, a new evolutionary learning algorithm is proposed by hybridizing the Taguchi method and chaos artificial bee colony (CABC). The algorithm is thus called HTCABC. First, the chaos search algorithm and adaptive bound method is adopted to improve the ABC performance and convergence rate. Then, the Taguchi method and crossover operation are incorporated into the CABC to produce good f...

Burgers’ equation with uncertain initial and boundary conditions is approximated using a polynomial chaos expansion approach where the solution is represented as a series of stochastic, orthogonal polynomials. Even though the analytical solution is smooth, a number of discontinuities emerge in the truncated system. The solution is highly sensitive to the propagation speed of these discontinuiti...

The results of extensive computations are presented to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular we follow the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos. As many as 13 period doublings are followed and used to compute the Feigenbaum number for the cascade and so enabl...

This paper studies the feasibility of CORSIA’s carbon neutral growth goal based on verified offsetting. It is motivated by an ongoing general debate about climate and regulatory integrity offsetting, thus systematically identifying critical offset characteristics. Using registry data from largest verifiers eligible under CORSIA, we show that majority offsets have minor integrity. challenges obj...

The route to chaos in a ̄uid layer heated from below is investigated by using the weak non-linear theory as well as Adomian's decomposition method to solve a system of ordinary di€erential equations which result from a truncated Galerkin representation of the governing equations. This representation yields the familiar Lorenz equations. While the weak non-linear method of solution provides sign...

A quantum chaos cloning multi-objective evolutionary algorithm was proposed herein based on chaos search ergodicity, quantum computing efficiency and clonal selection theory of antibodies in artificial immune system. The qubits encoded initial population is used in the new algorithm, Chaos quantum rotation gates are introduced to update individuals, crowding distance is used to keep solution po...

In this paper, a chaos search immune algorithm (CSIA) is proposed by integrating the chaos optimization algorithm and the clonal selection algorithm. First, optimization variables are expressed by chaotic variables through solution space transformation. Then, taking advantages of the ergodic and stochastic properties of chaotic variables, a chaos search is performed in the neighbourhoods of hig...

This paper describes the use of polynomial chaos expansions to approximate the probability of a collision between two satellites after at least one performs a translation maneuver. Polynomial chaos provides a computationally efficient means to generate an approximate solution to a stochastic differential equation without introducing any assumptions on the a posteriori distribution. The stochast...

In this paper, we solve the two-dimensional advection-diffusion equation with random transport velocity. The generalized polynomial chaos expansion is employed to discretize the equation in random space while the spectral/hp element method is used for spatial discretization. Numerical results which demonstrate the convergence of generalized polynomial chaos are presented. Specifically, it appea...