A nonlinear theory of wake development

A simple new series, using an expansion of the velocity profile in parabolic cylinder functions, has been developed to describe the nonlinear evolution of a steady, laminar, incompressible wake from a given arbitrary initial profile. The first term in this series is itself found to provide a very satisfactory prediction of the decay of the maximum velocity defect in the wake behind a flat plate or aft of the recirculation zone behind a symmetric blunt body. A detailed analysis, including higher order terms, has been made of the flat plate wake with a Blasius profile at the trailing edge. The same method yields, as a special case, complete results for the development of linearized wakes with arbitrary initial profile under the influence of arbitrary pressure gradients. Finally, for purposes of comparison, a simple approximate solution is obtained using momentum integral methods, and found to predict satisfactorily the decay of the maximum velocity defect. © 1970 Wolters-Noordhoff Publishing.

Some new concepts in nonlinear systems

Some new concepts characterizing the response of nonlinear systems are developed. These new concepts are denoted by the terms, the transient system equivalent, the response vector, and the space-phase components. This third concept is analyzed in comparison with the well-known technique of symmetrical components. The performance of a multiplicative feedback control system is represented by a nonlinear integro-differential equation; its solution is obtained by the principle of variation of parameters. The system response is treated as a vector and is resolved into its space-phase components. The individual effects of these components on the performance of the system are discussed. The suitability of the technique for the transient analysis of higher order nonlinear control systems is discussed.

Application of D transforms in the analysis of nonlinear distributed parameter systems

The scope of application of Laplace transforms presently limited to the study of linear partial differential equations, is extended to the nonlinear domain by this study. This has been achieved by modifying the definition of D transforms, put forth recently for the study of classes of nonlinear lumped parameter systems. The appropriate properties of the new D transforms are presented to bring out their applicability in the analysis of nonlinear distributed parameter systems.

L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria

A Recursive Perspective on Discursive Legitimation and Organizational Action in Mergers and Acquisitions

This paper challenges the predominant view that legitimation is merely a specific phase in merger or acquisition processes. We argue that a better understanding of postmerger organizational dynamics calls for conceptualization of discursive legitimation as an inherent part of unfolding merger processes. In particular, we focus on the recursive relationship between legitimation and organizational action. We have two objectives: to outline a theoretical model that helps one to understand the dynamics of discursive legitimation and organizational action in postmerger organizations, and to examine a revealing case to distinguish the inherent risks and problems in discursive legitimation. Our case analysis focuses on the merger between the French pharmaceutical companies BioMérieux and Pierre Fabre. We adopt a critical multimethod approach and distinguish specific discursive dynamics and pathological tendencies in this case. The analysis highlights the unintended consequences of discursive legitimation, the central role of sensegiving and sensehiding in discursive legitimation, the inherently political nature of legitimation and the risks associated with politicization, the special problems associated with fashionable discourses and the role of the media, the use of specific discursive strategies for legitimation and delegitimation, and the crucial role of actual integration results. This analysis adds to the existing research on mergers and acquisitions by treating discursive legitimation as part of the merger dynamics. In particular, our case analysis provides a new explanation for merger failure. We also believe that the recursive model connecting discursive legitimation and delegitimation strategies to concrete organizational action makes a more general contribution to our understanding of organizational legitimation.

Nonlinear aeroelasticity of rotating and flapping wings - a review

The interaction between large deflections, rotation effects and unsteady aerodynamics makes the dynamic analysis of rotating and flapping wing a nonlinear aeroelastic problem. This problem is governed by nonlinear periodic partial differential equations whose solution is needed to calculate the response and loads acting on vehicles using rotary or flapping wings for lift generation. We look at three important problems in this paper. The first problem shows the effect of nonlinear phenomenon coming from piezoelectric actuators used for helicopter vibration control. The second problem looks at the propagation on material uncertainty on the nonlinear response, vibration and aeroelastic stability of a composite helicopter rotor. The third problem considers the use of piezoelectric actuators for generating large motions in a dragonfly inspired flapping wing. These problems provide interesting insights into nonlinear aeroelasticity and show the likelihood of surprising phenomenon which needs to be considered during the design of rotary and flapping wing vehicle

Nonlinear vibration analysis of composite laminated and sandwich plates with random material properties

Nonlinear vibration analysis is performed using a C-0 assumed strain interpolated finite element plate model based on Reddy's third order theory. An earlier model is modified to include the effect of transverse shear variation along the plate thickness and Von-Karman nonlinear strain terms. Monte Carlo Simulation with Latin Hypercube Sampling technique is used to obtain the variance of linear and nonlinear natural frequencies of the plate due to randomness in its material properties. Numerical results are obtained for composite plates with different aspect ratio, stacking sequence and oscillation amplitude ratio. The numerical results are validated with the available literature. It is found that the nonlinear frequencies show increasing non-Gaussian probability density function with increasing amplitude of vibration and show dual peaks at high amplitude ratios. This chaotic nature of the dispersion of nonlinear eigenvalues is also r

A recursive perspective on discursive legitimation and organizational action in mergers and acquisitions

This paper challenges the predominant view that legitimation is merely a specific phase in merger or acquisition processes. We argue that a better understanding of postmerger organizational dynamics calls for conceptualization of discursive legitimation as an inherent part of unfolding merger processes. In particular, we focus on the recursive relationship between legitimation and organizational action. We have two objectives: to outline a theoretical model that helps one to understand the dynamics of discursive legitimation and organizational action in postmerger organizations, and to examine a revealing case to distinguish the inherent risks and problems in discursive legitimation. Our case analysis focuses on the merger between the French pharmaceutical companies BioMérieux and Pierre Fabre. We adopt a critical multimethod approach and distinguish specific discursive dynamics and pathological tendencies in this case. The analysis highlights the unintended consequences of discursive legitimation, the central role of sensegiving and sensehiding in discursive legitimation, the inherently political nature of legitimation and the risks associated with politicization, the special problems associated with fashionable discourses and the role of the media, the use of specific discursive strategies for legitimation and delegitimation, and the crucial role of actual integration results. This analysis adds to the existing research on mergers and acquisitions by treating discursive legitimation as part of the merger dynamics. In particular, our case analysis provides a new explanation for merger failure. We also believe that the recursive model connecting discursive legitimation and delegitimation strategies to concrete organizational action makes a more general contribution to our understanding of organizational legitimation.

Ratio transformer bridge for the measurement of dielectric constant of lossy liquids

A three-terminal capacitance bridge is developed for the measurement of the dielectric constant of lossy liquids. Using this modified ratio transformer bridge, the capacitance shunted by a resistance as low as 50 Omega is measured at 10 kHz. The capacitance error associated with the inductance of the connecting wire is compensated using the novel method of introducing an additional transformer to the existing ratio transformer bridge. Other sources of capacitance errors, such as the non-zero output impedence of the ratio transformer and the shield capacitances of the cables, are discussed.

Incremental attribute evaluation through recursive procedures

Incremental semantic analysis in a programming environment based on Attribute Grammars is performed by an Incremental Attribute Evaluator (IAE). Current IAEs are either table-driven or make extensive use of graph structures to schedule reevaluation of attributes. A method of compiling an Ordered Attribute Grammar into mutually recursive procedures is proposed. These procedures form an optimal time Incremental Attribute Evaluator for the attribute grammar, which does not require any graphs or tables.

Response of nonlinear systems to narrow-band excitation

The hardening cubic spring oscillator is studied under narrow-band gaussian excitation. Equivalent linearization leads to multiple steady states. The realizability of the solution is discussed through stochastic stability analysis. Theoretical results are supported by numerical simulation.

Performance analysis of a suprathreshold, stochastic resonance based nonlinear detector

In this paper we introduce a nonlinear detector based on the phenomenon of suprathreshold stochastic resonance (SSR). We first present a model (an array of 1-bit quantizers) that demonstrates the SSR phenomenon. We then use this as a pre-processor to the conventional matched filter. We employ the Neyman-Pearson(NP) detection strategy and compare the performances of the matched filter, the SSR-based detector and the optimal detector. Although the proposed detector is non-optimal, for non-Gaussian noises with heavy tails (leptokurtic) it shows better performance than the matched filter. In situations where the noise is known to be leptokurtic without the availability of the exact knowledge of its distribution, the proposed detector turns out to be a better choice than the matched filter.