Nonlinear Differential Equations (nonlinear + differential_equation)

Distribution by Scientific Domains

Selected Abstracts

An efficient method for analyzing nonuniformly coupled microstrip lines

Dengpeng Chen
Abstract This article presents an efficient method for analyzing nonuniformly coupled microstrip lines. By choosing a modal-transformation matrix, the coupled nonlinear differential equations describing the symmetric nonuniformly coupled microstrip lines are decoupled using even- and odd-mode parameters; the original problem is thus transformed into two single nonuniform transmission lines. A power-law function of arbitrary order and having two adjustable parameters is chosen to better approximate the equation coefficients. Closed-form ABCD matrix solutions are obtained and used to calculate the S -parameters of nonuniformly coupled microstrip lines. Numerical results for two examples are compared with those from a full-wave commercial package and experimental ones in the literature in order to demonstrate the accuracy and efficiency of this method. This highly efficient method is employed to optimize a cosine-shape 10-dB codirectional coupler, which has good return loss and high directivity performance over a wide frequency range. 2005 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2005. [source]

Dexterous manipulation of an object by means of multi-DOF robotic fingers with soft tips

Pham Thuc Anh Nguyen
This article analyzes the dynamics of motion of various setups of two multiple degree-of-freedom (DOF) fingers that have soft tips, in fine manipulation of an object, and shows performances of their motions via computer simulation. A mathematical model of these dynamics is described as a system of nonlinear differential equations expressing motion of the overall fingers-object system together with algebraic constraints due to tight area contacts between the finger-tips and surfaces of the object. First, problems of (1) dynamic, stable grasping and (2) regulation of the object rotational angle by means of a setup of dual two-DOF fingers, are treated. Second, the problem of regulating the position of the object mass center by means of a pair of two-DOF and three-DOF fingers is considered. Third, a set of dual three-DOF fingers is treated, in order to let it perform a sophisticated task, which is specified by a periodic pattern of the object posture and a constant internal force. In any case, there exist sensory-motor coordinations, which are described by analytic feedback connections from sensing to actions at finger joints. In the cases of setpoint control problems, convergences of motion to secure grasping together with the specified object rotational angle and/or the specified object mass center position, are proved theoretically. A constraint stabilization method (CSM) is used for solving numerically the differential algebraic equations to show performances of the proposed sensory-feedback schemes. 2002 Wiley Periodicals, Inc. [source]

Forced oscillation of second order superlinear differential equations

Yuan Gong Sun
Abstract In this paper, we establish some new criteria for the oscillation of second order forced nonlinear differential equations (r (t )x ,(t )), + p (t )x ,(t ) + q (t )f (x (t )) = e (t ) in both cases when q (t ) < 0 and q (t ) changes its sign. Our results are sharper than those of Agarwal and Grace [1], Cakmak and Tiryaki [2], Ou and Wong [17] for the second order case. ( 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Chemical networks with inflows and outflows: A positive linear differential inclusions approach

David Angeli
Abstract Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009 [source]