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Abstract: This paper investigates the stabilization of three dimensional chaotic systems in a finite time by extending our previous method for chaos stabilization. Based on the finite-time stability theory, a control law is proposed to realize finite-time stabilization of three dimensional chaotic systems. In comparison with the previous methods, the controller obtained by our method is simpler than those. Moreover, the method obtained in this paper is suitable for a class of three dimensional chaotic systems. The efficiency of the control scheme is revealed by some illustrative simulations. [Copyright &y& Elsevier]

This paper is devoted to the valuation of American multi-asset put options. It is well known that the American multi-asset put option satisfies a linear complementary problem (LCP) on an unbounded domain. We consider a penalty method in which the LCP could be reformulated into a nonlinear parabolic problem on an unbounded domain. For the unbounded computational domain, a perfectly matched layer (PML) technique is applied to truncate it. As to the resulting bounded domain problem related to the option, we use a semi-implicit finite element method (SIFEM) to solve it. The convergence of this method is analyzed in detail. Finally, we present some numerical simulations to show the validity and efficiency of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper considers the issues of both state estimation and unknown information reconstruction for a class of uncertain complex dynamical networks subject to unknown inputs. First, a robust adaptive sliding mode observer which can be used to estimate the states of complex networks through available measurement outputs is developed by employing both adaptive technique and sliding mode control approach. Second, a high-gain second-order sliding mode observer is considered to exactly estimate the derivatives of the output vectors in a finite time. Third, by using the estimates of the states and output derivatives, a kind of algebraic unknown input reconstruction method is proposed. Finally, some numerical simulation examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: The traditional scaled boundary finite-element method (SBFEM) is a rather efficient semi-analytical technique widely applied in engineering, which is however valid mostly for linear differential equations. In this paper, the traditional SBFEM is combined with the homotopy analysis method (HAM), an analytic technique for strongly nonlinear problems: a nonlinear equation is first transformed into a series of linear equations by means of the HAM, and then solved by the traditional SBFEM. In this way, the traditional SBFEM is extended to nonlinear differential equations. A nonlinear heat transfer problem is used as an example to show the validity and computational efficiency of this new SBFEM. [ABSTRACT FROM AUTHOR]

Abstract: The objective of this paper is to develop a realistic model for ice–structure interaction. To this end, the experiments made by Bridges et al. [Bridges FG, Hatzes A, Liu DNC. Structure, stability and evolution of Saturn’s rings. Nature 1984;309:333–5] in order to measure the coefficient of restitution for ice particles are thoroughly analyzed. One particularly troublesome aspect of the aforementioned experiments is fracture of the ice particles during a collision. In the present effort, the collisional properties of the ice particles are investigated using a Finite Element approach. It is found that a major challenge in modeling collision of the ice balls is the prediction of the onset of fracture and crack propagation in them. In simulations of a block of ice collision to a structure, it is crucial that fracture is determined correctly, as it will influence the collisional properties of the ice particles. The results of the simulation, considering fracture criterion implemented into the Finite Element Model [Zamankhan P, Bordbar M-H. Complex flow dynamics in dense granular flows. Part I: experimentation. J Appl Mech (T-ASME) 2006;73:648–57; Zamankhan P, Huang J. Complex flow dynamics in dense granular flows. Part II: simulations. J Appl Mech (T-ASME) 2007;74:691–702] together with a material model for the ice, imply that most of the kinetic energy dissipation occurs as a result of fracturing at the contact surface of the ice particles. The results obtained in the present study suggest that constitutive models such as those proposed by Brilliantov et al. [Brilliantov NV, Spahn F, Hertzsch JM, Poschel T. Model for collisions in granular gases. Phys Rev E;1996;53:5382–92] for collisions of ice particles are highly questionable. [Copyright &y& Elsevier]